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 chocolates bar 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

Rasheed bought 9 packages of chocolates bar.

Explanation:

Let C be the number of packages of chocolate bars.

Let T be the number of packages of toffee bars.

Rasheed handed out 2/3 of 2C of the chocolate bars and 3/5 of 2T of the toffee bars.

(1) Rasheed bought 1 fewer package of chocolate bars than toffee bars.

Equation becomes:

`C=T-1` .....(1)

(2) Rasheed handed out the same number of each kind of candy bar .

Equation becomes:

`(2)/(3)* 2C =(3)/(5)* 2T`

=>
`(4C)/(3) =(6T)/(5)`

=>
`20C=18T`

=>
`20C-18T=0`

Taking out 2 common, we get

`10C-9T=0` ......(2)

Substituting
`C=T-1` in (2)

`10(T-1)-9T=0`

=>
`10T-10-9T=0`

=>
`T-10=0`

T = 10

As
`C=T-1`

`C=10-1`

C = 9

Therefore, Rasheed bought 9 packages of chocolates bar.