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 boxe

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 :))

Using f for Fred and j for Joe:

Fred initially had 240 boxes.

Edited to correct error!

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Oh dear, Alan and I have different answers.

Maybe we interpreted something differently :/

Melody your answer is right but um Alan yours is kinda wrong but u still tried cmon cheer up please😄

Yes, I realised my error as soon as I posted it!  I've now corrected it.

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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    →     this is what Fred started with