Fred and Joe had a total of 432 match boxes. Fred gave 2/5 of his match boxes to Joe and then Joe gave 1/4 of the total number of match boxes she had to Fred. Both of them had the same number of match boxes in the end. How many match boxes did Fred have at first?

Guest Aug 15, 2015

#2**+10 **

Fred and Joe had a total of 432 match boxes. Fred gave 2/5 of his match boxes to Joe and then Joe gave 1/4 of the total number of match boxes she had to Fred. Both of them had the same number of match boxes in the end. How many match boxes did Fred have at first?

Fred had F Joe had 432-F

Fred gave 2/5 (0.4) of his match boxes to Joe

So now Fred has 0.6F and Joe has 432-F+0.4F = 432-0.6F

then Joe gave 1/4 of the total number of match boxes she had to Fred

So now Fred has 0.6F+0.25(432-0.6F) = 0.6F+108-0.15F = 0.45F+108

And Joe has 0.75(432-0.6F)=324-0.45F

Both of them had the same number of match boxes in the end.

324-0.45F=0.45F+108

216 = 0.9F

F =240

**So fred had 240 to start with.**

Check :

If fred had 240 then Joe had 432-240= 192

Fred gave 2/5 of 240 = 96 to Joe

so Fred now has 240-96=144 and Joe has 192+96=288

Joe have a 1/4 to Fred

Fred now has 144+(1/4 of 288) = 216 and Jow has (3/4) * 288 = 216

GOOD They have botyh got the same :))

Melody
Aug 15, 2015

#1**+10 **

Using f for Fred and j for Joe:

Fred initially had 240 boxes.

Edited to correct error!

.

Alan
Aug 15, 2015

#2**+10 **

Best Answer

Fred and Joe had a total of 432 match boxes. Fred gave 2/5 of his match boxes to Joe and then Joe gave 1/4 of the total number of match boxes she had to Fred. Both of them had the same number of match boxes in the end. How many match boxes did Fred have at first?

Fred had F Joe had 432-F

Fred gave 2/5 (0.4) of his match boxes to Joe

So now Fred has 0.6F and Joe has 432-F+0.4F = 432-0.6F

then Joe gave 1/4 of the total number of match boxes she had to Fred

So now Fred has 0.6F+0.25(432-0.6F) = 0.6F+108-0.15F = 0.45F+108

And Joe has 0.75(432-0.6F)=324-0.45F

Both of them had the same number of match boxes in the end.

324-0.45F=0.45F+108

216 = 0.9F

F =240

**So fred had 240 to start with.**

Check :

If fred had 240 then Joe had 432-240= 192

Fred gave 2/5 of 240 = 96 to Joe

so Fred now has 240-96=144 and Joe has 192+96=288

Joe have a 1/4 to Fred

Fred now has 144+(1/4 of 288) = 216 and Jow has (3/4) * 288 = 216

GOOD They have botyh got the same :))

Melody
Aug 15, 2015

#3**0 **

Oh dear, Alan and I have different answers.

Maybe we interpreted something differently :/

Melody
Aug 15, 2015

#4**+5 **

Melody your answer is right but um Alan yours is kinda wrong but u still tried cmon cheer up pleaseðŸ˜„

Guest Aug 15, 2015

#6**+5 **

Let x be the number of match boxes that Fred started with....then, Joe had 432 - x

And we know that :

x - (2/5)x + (1/4)[(432 -x) +(2/5)x] = [ (432 -x) + (2/5)x - (1/4)[(432 - x) +(2/5)x] simplify

x - (2/5)x + 108 - (1/4)x + (1/10)x = 432 -x + (2/5)x - 108 +(1/4) x - (1/10)x

108 + (9/20)x = 324 - (9/20)x

(18/20)x = 216

(9/10)x = 216 multiply both sides by (10/9)

x = 240 â†’ this is what Fred started with

CPhill
Aug 15, 2015