Question

the ratio of peas Julia had to a number of peas Vlada had was 3:2 after Julia gave 15 peas, she still has 10 more peas than Vlada. How many peas did Julia have at first?

Answer 1

Julia had 120 peas to start .

Answer 2

120 peas

Explanation:

Before Julia gave Vlada 15 peas, the ratio of their numbers was 3:2. Afterward, Julia still had 10 more peas. You want to know the number Julia started with.

Solution

Let j represent the initial number of peas Julia had. Then Vlada had 2/3j peas. After the transfer, the difference was ...

(j -15) -(2/3j +15) = 10

1/3j -30 = 10

1/3j = 40

j = 120

Julia had 120 peas at first.

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Additional comment

The transfer of peas decreases the difference by 30, so if it remains 10 it must have originally been 40. The difference in initial ratio units is 3-2 = 1, so Julia's initial 3 ratio units represent 3·40 = 120 peas.

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