Danny has boxes colored either red or blue. In each blue box

BTGmoderatorLU wrote:Source: Economist GMAT

Danny has boxes colored either red or blue. In each blue box, there is a fixed number of blueberries. In each red box, there is a fixed number of strawberries. If Danny disposed of one blue box for one additional red box, the total number of berries (of both kinds) would increase by 25, and the difference between the total number of strawberries and the total number of blueberries would increase by 95. Each blue box contains how many blueberries?

A. 35
B. 40
C. 45
D. 50
E. 60

The OA is A

Say there are x number of blue boxes and each blue box contains y number of blueberries; similarly, there are a number of red boxes and each blue box contains b number of strawberries,

Thus,

the total number of blueberries = xy; and

the total number of strawberries = ab

total number of berries before = xy + ab ---(1)

As per the condition, the number of blue boxes = (x – 1) and the number of red boxes = (a + 1)

the total number of blueberries = (x –1)y; and

the total number of strawberries = (a + 1)b

total number of berries now = (x –1)y + (a + 1)b ---(2)

As per the information, "the total number of berries (of both kinds) would increase by 25," we have

[(x –1)y + (a + 1)b] – [xy + ab] = 25

xy – y + ab + b – xy – ab = 25

b – y = 25 ---(3)

As per the information, "the difference between the total number of strawberries and the total number of blueberries would increase by 95," we have

[(x –1)y – (a + 1)b] – [xy – ab] = 95

xy – y – ab – b – xy + ab = 95

b + y = 95 ---(4)

From (3) and (4), we have

y = number of blueberries in each blue box = 35

The correct answer: A

Hope this helps!

-Jay
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BTGmoderatorLU wrote:Source: Economist GMAT

Danny has boxes colored either red or blue. In each blue box, there is a fixed number of blueberries. In each red box, there is a fixed number of strawberries. If Danny disposed of one blue box for one additional red box, the total number of berries (of both kinds) would increase by 25, and the difference between the total number of strawberries and the total number of blueberries would increase by 95. Each blue box contains how many blueberries?

A. 35
B. 40
C. 45
D. 50
E. 60

The OA is A

We can let b = the number of blueberries in each blue box and m = the number of blue boxes. Likewise, we can let r = the number of strawberries in each red box and n = the number of red boxes.

So the total number of blueberries and strawberries is bm + rn.
We are told that if Danny disposed of one blue box for one additional red box, the total number of berries (of both kinds) would increase by 25. So we can create the equation:

b(m - 1) + r(n + 1) = bm + rn + 25

bm - b + rn + r = bn + rn + 25

-b + r = 25

r = 25 + b

We are also told that the difference between the total number of strawberries and the total number of blueberries would increase by 95. So we can create the equation:

r(n + 1) - b(m - 1) = rn - bm + 95

rn + r - bm + b = rn - bm + 95

r + b = 95

Since r = 25 + b, we have:

25 + b + b = 95

2b = 70

b = 35

Answer: A