SOLUTION: A box had twice as many grapes as a basket. After 2 kilograms were added to the basket it contained 0.5 kilograms more than the box. How many kilograms of grapes did the basket con

Question 1054869: A box had twice as many grapes as a basket. After 2 kilograms were added to the basket it contained 0.5 kilograms more than the box. How many kilograms of grapes did the basket contain?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
if the box contains twice as many grapes as the basket, then the weight of the grapes in the box must be twice the weight of the grapes in the basket.

if you let x equal the weight of the grapes in the box and y equal the weight of the grapes in the basket, then you get x = 2y.

when you add 2 kilograms of grapes to the basket, then the weight of the grapes in the basket becomes y + 2.

the weight of the grapes in the box remains the same at x.

since the weight of the grapes in the basket now weighs .5 kilograms more than the weight of the grapes in the box, you get y + 2 = x + .5

since you know that x = 2y, then replace x with 2y in the equation of y + 2 = x + .5 to get y + 2 = 2y + .5

subtract y from both sides of this equation and subtract .5 from both sides of this equation and solve for y to get y = 1.5.

since x = 2y, this means that x = 3.

x represents the weight of the grapes in the box.
y represents the weight of the grapes in the basket.

you start off with 3 kilograms of grapes in the box and 1.5 kilograms of grapes in the basket.

you add 2 kilograms to the weight of the grapes in the basket to get 3 kilograms of grapes in the box and 3.5 kilograms of grapes in the basket.

the basket now contains .5 more kilograms of grapes than what's in the box.

the solution seems reasonable to me.

the problem was not worded that well.
that made it a little difficult to understand.

since the weight of the box without anything in it and the weight of the basket without anything in it could have been different, then considering the weight of the box itself and the weight of the basket itself would have complicated the problem to where it couldn't be solved.

by assuming that the problem was talking about the weight of the grapes in the box and the weight of the grapes in the basket, the problem became manageable.

consequently, i made that assumption and then the problem made more sense, at least to me.

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