Question

Amy, Bruce, and Carlos collected a total of 168 pounds of cans to recycle. Bruce collected 1/3 the number of pounds of cans Carlos collected. Amy collected the same number of pounds of cans as Bruce and Carlos combined. Solve the equation for c, and then determine the number of pounds of cans Bruce collected.. Show all work necessary to support your answer

Answer 1

Answer:

$c = 63\\b=21$

Step-by-step explanation:

Let number of pounds of cans collected by Amy = $a$

Let number of pounds of cans collected by Bruce = $b$

Let number of pounds of cans collected by Carlos = $c$

As per question statement, total number of cans collected = 168

$a+b+c=168$ ..... (1)

Number of pounds collected by Bruce is $\frac{1}{3}$rd of the pounds of cans collected by Carlos.

$b = \dfrac{1}{3}c ..... (2)$

Number of pounds collected by Amy is equal to number of pounds collected by Bruce and Carlos combined.

$a = b+c$

Using equation (2):

$a = \dfrac{1}{3}c +c \\\Rightarrow a =\dfrac{4}{3}c ..... (3)$

Using equations (2) and (3) in equation (1), we get:

$\dfrac{4}{3}c+\dfrac{1}{3}c+c =168\\\Rightarrow \dfrac{8}{3}c = 168\\\Rightarrow c =63$

Using equation (2):

$b = \dfrac{63}{3} = 21$