Question

Rasheed bought two kinds of candy bars, chocolate and toffee, that came in packages of 2 bars each. He handed out \frac{2}{3} of the chocolate bars and \frac{3}{5} of the toffee bars. How many packages of chocolate bars did Rasheed buy?

Answer 1

Rasheed bought 9 packages of chocolate bars

Step by step explanation:

Let x represent the number of packages of chocolate bars

and y represent the number of packages of toffee bars.

Rasheed handed out 2/3 × 2x of the chocolate bars

and

3/5 × 2y of the toffee bars.

Rasheed bought 1 fewer package of chocolate bars than toffee bars

=> x = y - 1 ...........................(1)

Rasheed handed out the same number of each kind of candy bar

=>2/3 × 2x = 3/5 × 2y

4x/3 = 6y/5

x = (3/4)(6y/5) = 9y/10...................(2)

Using the value of x in (2) in (1)

9y/10 = y - 1

(1 - 9/10)y = 1

(1/10)y = 1

y = 10

Therefore, y is 10 and x is 9

Answer 2

Rasheed bought 9 packages of chocolate bars

Explanation:

Rasheed bought two kinds of candy bars, chocolate and toffee, that came in packages of 2 bars each.

Let 'cb' represent the number of chocolate bars that Rasheed bought

Let 'tb' represent the number of toffee bars that Rasheed bought

If Rasheed bought 1 fewer package of chocolate bars than toffee bars; we have the following suitable expression

cb = tb - 1

Also; he handed out
`(2)/(3)` of the cb and
`(3)/(5)` of tb; we have:

`(2)/(3) *cb = (3)/(5)*tb`

`10cb = 9tb`

If we make tb the subject of the formula since we are only looking for the number of chocolate bars Rasheed bought; we have:

`tb=(10)/(9) cb`

From the previous expression cb = tb - 1

1 = tb - cb

Replacing
`tb=(10)/(9) cb` in the above equation; we have:

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

`1 = (1cb-9cb)/(9)`

`1 = (1cb)/(9)`

`cb = 1*9`

cb = 9

Hence,Rasheed bought 9 packages of chocolate bars