Question

Rasheed bought two kinds of candy bars, chocolate and toffee, that came in packages of 2 bars each. He handed out 2/3 of the chocolate bars and 3/5 of the toffee bars. How many packages of chocolate bars did Rasheed buy? (1) Rasheed bought 1 fewer package of chocolate bars than toffee bars. (2) Rasheed handed out the same number of each kind of candy bar.

Answer 1

9 packages of chocolate bars

Explanation:

Let he bought c packages of chocolate bars and t packages of toffee bars,

Since, he bought 1 fewer package of chocolate bars than toffee bars.

⇒ c = t - 1 -----(1)

Also, he handed out out
`(2)/(3)` of the chocolate bars and
`(3)/(5)` of the toffee bars,

If he handed out the same number of each kind of candy bar.

`\implies (2)/(3)* c=(3)/(5)* t`

`10c = 9t` ( By cross multiplication )

`\implies t=(10)/(9)c` ( Division property of equality )

From equation (1),

`c=(10)/(9)c-1`

`1=(10)/(9)c-c`

`1=(10c-9c)/(9)`

`1=(c)/(9)`

`\implies c = 9`

Hence, he bought 9 packages of chocolate bars.