Question

The ratio of Victoria's weight was 4:5. If Victoria's weight increased by 5 lb. and Kazuki's weight decreased by 1lb., Victoria would have the same weight as Kazuki. What was Victoria's original weight?

Answer 1

24 lb

Explanation:

The given relations can be used to write a system of equations for the two weights.

Setup

Let v and k represent Victoria's and Kazuki's original weights. The original ratio is ...

v/k = 4/5

After the change, the weights are equal:

v +5 = k -1

Solution

Adding 1 to the second equation, we have ...

v +6 = k

Substituting for k in the first equation gives ...

v/(v+6) = 4/5

5v = 4v +24 . . . . . multiply by 5(v+6)

v = 24 . . . . . . . . . subtract 4v

Victoria's original weight was 24 pounds.

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Additional comment

Kazuki's original weight was 30 lb. After the changes in weight, both weighed 29 lb.