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

Answer:

Rasheed bought 9 packages of chocolates bar.

Step-by-step 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:

$\frac{2}{3}\times 2C =\frac{3}{5}\times 2T$

=> $\frac{4C}{3} =\frac{6T}{5}$

=> $20C=18T$

=> $20C-18T=0$

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.