Question

The ratio of Shauntay's cards to Jessica's cards is 5 to 3. After Shauntay gives Jessica 12 of her cards, both girls have the same number of cards. How many cards do Shauntay and Jessica each have now (that the number is equal)?

Answer 1

They have 48 cards.

Explanation:

let s be the number of Shauntay's cards and j be the number of Jessica's cards.

The ratio of Shauntay's cards to Jessica's cards is 5 to 3, then

(1)
`(s)/(j)` =
`(5)/(3)`

After Shauntay gives Jessica 12 of her cards, both girls have the same number of cards, then

(2) s-12 =j+12.

From (2), we get s= j+24. If we put j+24 instead of s in (1) we get:

`(j+24)/(j)` =
`(5)/(3)`

3×j+24×3 = 5×j From this we get;

2×j=72 and j=36

After Shauntay gives Jessica 12 of her cards, Shauntay and Jessica would have 48 cards.