Peaches varied directly as apples. when there were 40 peaches, there were 120 apples. how many apples went with 500 peaches?

Given that p eaches varied directly as apples. then:

let the number of peaches be p and that of apples be a

hence

p=ka

where

k is constant of proportionality given by:

k=p/a

when:

p=40, a=120

thus

k=40/120=1/3

thus the equation will be:

p=1/3a

thus the number of apples where there are 500 peaches will be:

500=1/3a

multiplying both sides by 3 we get:

500 * 3=1/3a*3

a=1500