Question

Jim and Alvin have a total of 360 Pokemon cards.

The ratio of the number of Jim's cards to the number of Alvin's cards is 7:2
Alvin buys some cards from Jim.
The ratio of the number of Jim's cards to the number of Alvin's cards is now 7:5
How many cards does Alvin buy from Jim?

Answer 1

70 cards bought from Jim

Explanation:

the ratio of cards Jim : Alvin = 7 : 2 = 7x : 2x ( x is a multiplier ) , then

7x + 2x = 360

9x = 360 ( divide both sides by 9 )

x = 40

Jim has 7 × 40 = 280 cards

Alvin has 2 × 40 = 80 cards

let n be the number of cards Alvin buys from Jim , then

Jim has 280 - n cards

Alvin has 80 + n cards

Then expressing in fractional form

`(280-n)/(80+n)` =
`(7)/(5)` ( cross- multiply )

7(80 + n) = 5(280 - n) ← distribute both parenthesis

560 + 7n = 1400 - 5n ( add 5n to both sides )

560 + 12n = 1400 ( subtract 560 from both sides )

12n = 840 ( divide both sides by 12 )

n = 70

Alvin buys 70 cards from Jim