confusing algebra

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nanase

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Hi, my son got this question in his school and I would like to help him best I can :
John has 276 apples and bananas. He sold the same number of apples and bananas and had 2/5 of the apples and 2/7 of the bananas left. How many bananas does he have left?

I can only set x as apples and y as bananas, and x+y=276. need help in setting the next equations. I wonder whether I should set other variables? I did try and things get more complicated...
 
Last edited:
nanaseailie said:
Hi, my son got this question in his school and I would like to help him best I can :
John has 276 apples and bananas. He sold the same number of apples and bananas and had 2/5 of the apples and 2/7 of the bananas left. How many bananas does he have left?

I can only set x as apples and y as bananas, and x+y=276. need help in setting the next equations. I wonder whether I should set other variables? I did try and things get more complicated...
Click to expand...
Presumably you saw that 3/5 of the apples has to equal 5/7 of the bananas.
 
Oh, darn! Well since I just cannot resist:
Let x be the number of apples and y the number of bananas.
"John has 276 apples and bananas."
x+ y= 276
" He sold the same number of apples and bananas"
Let z be the number of apples and bananas sold.
So he had x- z apples and y- z bananas.
"and had 2/5 of the apples and 2/7 of the bananas left."
x- z= (2/5)x which is equivalent to z= (3/5)x.
y- z= (2/7)y which is equivalent to z= (5/7)y.

z= (3/5)x= (5/7)y so 21x= 25y. We also have x+ y= 276.
x= (25/21)y so (25/21)y+ y= (25/21+ 21/21)y= (46/21)y= 276,
y= (21/46)(276)= (21)(6)= 126, (The fact that this is an integer is very reassuring!)
He initially had 126 bananas.

" How many bananas does he have left?"
After selling bananas he had 2/7 of the bananas left,
(2/7)(126)= 2(18)= 36.
He had 36 bananas left,

Check:
If he initially had 126 bananas then he had 276- 126= 150 apples,
If he had 2/5 of the apples left then he had (2/5)(150)= 60 apples left.

So he sold 126-36= 90 bananas and 150- 60= 90 apples,

Yes! He sold the same number of apples and bananas as required!
 
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