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

Answer:

9 packages of chocolate bars

Step-by-step 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 $\frac{2}{3}$ of the chocolate bars and $\frac{3}{5}$ of the toffee bars,

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

$\implies \frac{2}{3}\times c=\frac{3}{5}\times t$

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

$\implies t=\frac{10}{9}c$    ( Division property of equality )

From equation (1),

$c=\frac{10}{9}c-1$

$1=\frac{10}{9}c-c$

$1=\frac{10c-9c}{9}$

$1=\frac{c}{9}$

$\implies c = 9$

Hence, he bought 9 packages of chocolate bars.