OPINION
DONALD RUSSELL, Circuit Judge:Plaintiff William Sailor appeals the district court’s dismissal, after a bench trial, of his claims against his former employer, Hubbell Incorporated (“Hubbell”),1 under the Age Discrimination in Employment Act, 29 U.S.C. §§ 621-634 (“ADEA”), and argues that the district court committed reversible error by refusing to give him a jury trial. While we agree that the district court should have allowed Sailor to try his case before a jury, we find the evidence of discrimination presented by Sailor at the bench trial to have been so lacking in substance that no reasonable jury could have found in his favor. Accordingly, we conclude that the district court’s error was harmless and affirm.
I.
Hubbell terminated Sailor in 1989 when Sailor was sixty-four years of age. After unsuccessfully pursuing age discrimination charges with the Equal Employment Opportunity Commission, Sailor brought ADEA claims against Hubbell in the Eastern District of Virginia, seeking a permanent injunction to prevent the defendant from continuing to violate his rights, back pay, reinstatement in his job and pension plan, front pay if reinstatement was not appropriate, liquidated damages, and attorneys’ fees. In his complaint, he demanded a jury.
Over Sailor’s objection, the district court dismissed the jury before trial, finding that all of Sailor’s claims were equitable except his claim for liquidated damages, and the liquidated damages claim was for “a sum certain.” At the bench trial, Sailor offered the testimony of several former Hubbell employees who gave accounts of age discrimination against them during their employment but introduced no evidence that his firing was motivated by his age. Hubbell presented extensive evidence that it had laid off workers because of declining business and Sailor had been chosen because his job performance had been the lowest among similarly-situated employees.
Twice during the trial — once after Sailor had finished presenting his evidence and once at the conclusion of the trial — Hubbell *325moved for judgment as a matter of law.2 In both instances, the district court took Hub-bell’s motion under consideration.
After all the evidence had been presented, the district court made the following factual findings, which we accept as conclusive because they were not challenged by Sailor in this appeal. Despite being promoted to the position of regional sales manager by the time he was laid off, Sailor had a long history of negative attitude, disruptive behavior, and poor sales performance throughout his tenure at Hubbell. His superiors made numerous efforts over, the years to work with these problems but were twice forced to consider firing him and, in 1987, placed him on six months probation. Following his probation, Sailor’s attitude improved but his sales volume did not.
Hubbell experienced deteriorating business beginning in 1986. The downturn continued through 1989, when Hubbell’s management decided that, as part of a long series of layoffs that affected its employees of all ages equally, it needed to lay off one of the five regional sales managers in one of its divisions, all of whom were over the age of forty. Because Sailor ranked last in this group in both sales volume and attitude, he was terminated.
Based on these findings, the district court held that Sailor had not established a violation of the ADEA and dismissed his case.
II.
We first address whether the district court’s dismissal of the jury violated Sailor’s right under the ADEA to a jury trial.3 We conclude that it did.
The ADEA states that “a person shall be entitled to a trial by jury of any issue of fact in any .>.. action for recovery of amounts owing as a result of a violation of [the ADEA], regardless of whether equitable relief is sought by any party in such action.” 29 U.S.C. § 626(c)(2). Section 626(c)(2) has been interpreted to allow parties a jury trial on legal claims but not equitable claims. Duke v. Uniroyal, Inc., 928 F.2d 1413, 1422 (4th Cir.), cert. denied, — U.S. -, 112 S.Ct. 429, 116 L.Ed.2d 449 (1991); Fortino v. Quasar Co., 950 F.2d 389, 398 (7th Cir.1991); E.E.O.C. v. Corry Jamestown Corp., 719 F.2d 1219, 1223-24 (3d Cir.1983). “When both legal and equitable remedies are demanded, the appropriate method of proceeding requires submission of the ease first to the jury to resolve liability and all legal damages. Thereafter, the court conducts a trial in equity to resolve all issues of equitable relief.” Duke, 928 F.2d at 1422.
Here, Sailor sought a permanent injunction against Hubbell, back pay, reinstatement in his job and pension plan, front pay if reinstatement was not appropriate, and liquidated damages. The injunction, reinstatement, and front pay are equitable forms of relief under the ADEA. Id. at 1424. However, a back pay award given under the *326ADEA is a legal remedy, Pons v. Lorillard, 549 F.2d 950, 953 (4th Cir.1977), aff'd, 434 U.S. 575, 582413, 98 S.Ct. 866, 871-72, 55 L.Ed.2d 40 (1978); see also Terry v. Chauffeurs, Teamsters and Helpers, Local 391, 863 F.2d 334, 339 n. 2 (4th Cir.1988), aff'd, 494 U.S. 558, 110 S.Ct. 1339, 108 L.Ed.2d 519 (1990); Troy v. City of Hampton, 756 F.2d 1000, 1003 (4th Cir.) (en banc), cert. denied, 474 U.S. 864, 106 S.Ct. 182, 88 L.Ed.2d 151 (1985); 1 Dan B. Dobbs, Law of Remedies § 2.6(3), at 166-67 & n. 61 (1993),4 as is an award of liquidated damages, Petrelle v. Weirton Steel Corp., 953 F.2d 148, 150 (4th Cir.1991); Lindsey v. American Cast Iron Pipe Co., 810 F.2d 1094, 1097 n. 3 (11th Cir.1987); Goodman v. Heublein, Inc., 645 F.2d 127, 129-30 n. 2 (2d Cir.1981). Accordingly, whether Hubbell is liable for discrimination against Sailor, as well as the appropriate amount of back pay and liquidated damages if Hubbell was found liable, were properly questions for a jury. The district court, therefore, erred in refusing Sailo.r a jury trial.5
III.
That Sailor should have been allowed to try his case before a jury, however, does not end our inquiry. We need not reverse the district court’s dismissal unless its denial of a jury was harmful to Sailor. Fed. R.Civ.P. 61; Atwood v. Pacific Maritime Ass’n, 657 F.2d 1055, 1058 (9th Cir.1981). We conclude that it was not.
Had Sailor been allowed to present his ADEA claims before a jury, the district court would properly have ordered judgment as a matter of law against-him. To succeed on his ADEA claims, Sailor had to show that he would not have been terminated but for Hub-bell’s intentional discrimination against him on account of his age, Goldberg v. B. Green and Co., Inc., 836 F.2d 845, 847 (4th Cir.1988), or, stated differently, that age was “a determining factor” in his termination, Duke, 928 F.2d at 1417. Sailor could have proven this discrimination in one of two ways. Goldberg, 836 F.2d at 847. First, he could have shown under “ordinary principles of proof’ that terminating him was the result of purposeful age discrimination. Id. (quotations omitted). Alternatively, Sailor could have used “the judicially-created proof scheme” developed in the Title VII context which has been adapted for ADEA cases. Id. at 847-48-(quotations omitted). Under it, he could- have made out a prima facia case against Hubbell by showing:
(1) that. he [was] in the protected age group [over 40], (2) that he was discharged, (3) that at the time of the discharge, he was performing his job at a level that met [Hubbell’s] legitimate expectations, and (4) that persons outside the protected age class were retained in the same position or that there was some other evidence .that [Hubbell] did not treat age neutrally in deciding to dismiss [him].
Herold v. Hajoca Corp., 864 F.2d 317, 319 (4th Cir.1988), cert. denied, 490 U.S. 1107, 109 S.Ct. 3159, 104 L.Ed.2d 1022 (1989). Hubbell then could have rebutted Sailor’s prima facia ease by showing that it had nondiscriminatory reasons for firing Sailor that Sailor could not demonstrate were pre-textual or untrue. E.E.O.C. v. Western Electric Co., Inc., 713 F.2d 1011, 1014 (4th Cir.1983).
No reasonable jury could have rendered a verdict for Sailor under either method of *327proof. Under ordinary principles of proof, no reasonable jury could have found that Sailor demonstrated by a preponderance, of the evidence that his age was a determining factor in his termination because Sailor offered no evidence that his termination was motivated by his age.
Nor could Sailor have won a verdict from reasonable jurors under the judicially-created proof scheme. Sailor could not have established a prima facia case because he could not have met part (4) of the test, as those retained in his job were all over age 40 and he showed no evidence that his age was not treated neutrally in his firing. Moreover, even if Sailor had established a prima facia case, reasonable jurors could only have found that Hubbell successfully rebutted it by showing that it had . terminated Sailor ’because a business downturn had forced it to lay off employees in Sailor’s position and Sailor had the worst performance among these employees.
In short, had the district court allowed Sailor to try his case before a jury, the jury would not have decided any portion of Sail- or’s claims because the district court properly would have granted judgment as a matter of law for Hubbell. We therefore, find-harmless the district court’s error in denying Sail- or a jury trial and affirm its dismissal of his claims.6
AFFIRMED.
. Hubbell Inc. is referred to as Pulsecom or Pulse Communications, Inc., throughout the record and the briefs. Because the various different corporate entities are not relevant to the merits here, we will, for simplicity, refer to all of them as "Hubbell.”
. Because this was a bench trial, not a jury trial, Hubbell's motions should have been for involuntary dismissal under Fed.R.Civ.P. 52(c), not for judgment as a matter of law under Fed.R.Civ.P. 50(a). However, the mistake was a technicality and it can safely be assumed that the judge treated Hubbell’s motion as a Rule 52(c) motion. See 9 Charles A. Wright and Arthur R. Miller, Federal Practice and Procedure: Civil § 2371, at 220 (1971) (stating that the mistake of using the wrong name on these motions should be disregarded).
. Hubbell contends that Sailor, despite properly demanding a jury under Fed.R.Civ.P. 38(b), waived his right to a jury trial by failing to object properly when the judge dismissed the jury. We reject this contention.
A party may waive its right to a jury trial after it has properly demanded a jury under Rule 38(b) if it ”fail[s] to object to the district court's decision to determine thedispositive issues of fact in th[e] case without a jury or to in any way remind the district court of [its] earl[ier] demand for a jury trial." United States v. 1966 Beechcraft Aircraft Model King Air A90, etc., 777 F.2d 947, 951 (4th Cir.1985). The party makes the necessary objection if it "at the time the ruling or order of the court is made ..., makes known to the court ... [its] objection to the action of the court and the grounds therefor.” Fed.R.Civ.P. 46.
Here, when the district court proposed sua sponte to dismiss the jury, Sailor’s counsel made known to the court her objection to its action and set forth numerous grounds on which her objection relied. Sailor, thus, easily complied with the requirements of Rule 46 and did not waive his right to a jury trial.
. The dissenting opinion in Hubbard v. Administrator, E.P.A., 982 F.2d 531, 547 (D.C.Cir.1992) (en banc) (Edwards, J.), cites this Court's opinion in Cline v. Roadway Express, Inc., 689 F.2d 481, 488-90 (4th Cir.1982), as “recognizing [the] equitable nature of back pay award [s] under [the] Age Discrimination in Employment Act.” The Court in Cline, however, did not recognize that back pay awards under the ADEA are equitable as opposed to legal — in fact, that issue was not even before it — and, as we have indicated, the law in this circuit is to the contrary.
. The district court appears to have determined that a jury was not necessary for two reasons. First, it concluded that an award of back pay was an equitable rather than a legal remedy; as previously stated, however, in ADEA actions, back pay is a legal remedy, Lorillard, 549 F.2d at 953. Second, it recognized that liquidated damages were normally a legal remedy for which a plaintiff was entitled to a jury, but found that no jury was necessary here because the liquidated 'damages requested were for a sum certain. This conclusion was also incorrect. Even if a jury was not needed to determine the amount of liquidated damages, Sailor was entitled to have a jury determine Hubbell’s liability for liquidated damages because liquidated damages are a legal remedy. See Duke, 928 F.2d at 1422.
. Hubbell appears to believe that, in order for us to conclude that the district court's error was harmless (i.e. that, even if the district court had allowed a jury, it would have ordered judgment as a matter of law for Hubbell under Fed. R.Civ.P. 50(a)), we must find that the district court erred in not ruling on its motion under Fed.R.Civ.P. 52(c) for involuntary dismissal during the bench trial. Acting on this belief, Hub-bell has cross-appealed the district court’s failure to grant an involuntary dismissal.
The district court’s action in not ruling on Hubbell’s motion for involuntary dismissal under Rule 52(c), however, is irrelevant to whether, with a jury, the district court properly would have ordered judgment as a matter of law under Rule 50(a). After Sailor presented his evidence, the district court properly could have found in favor of Hubbell and ordered involuntary dismissal under Rule 52(c). At the same time, the district court was also free’-"to decline to render any judgment until the close of all evidence,” even if it concluded at the close of Sailor’s evidence that it could not give a verdict in his favor. Fed.R.Civ.P. 52(c); Wright and Miller, supra note 2, § 2371, at 222. As a result, the district court’s refusal to rule on the motion for involun-’taiy dismissal does not imply that it would have denied a motion for judgment as a matter of law in a jury trial — in fact, it does not imply that the district court made any finding whatsoever with respect to Sailor’s evidence.
Hubbell’s cross-appeal was, therefore, unnecessary. In light of our affirmance of the district court’s dismissal of Sailor’s claim, we dismiss the cross-appeal as moot. We deny Sailor’s motion for attorneys' fees associated with the cross-appeal.