# Suppose you have two bags, A and B, with a total weight of 27 pounds, and you know that bag B weighs 3 pounds more that twice as much as A. How much do each of the bags weigh?

Feb 6, 2017

A: $8$ pounds
B: $19$ pounds

#### Explanation:

Let $A$ be the weight of bag A and $B$ be the weight of bag B.

If B is 3 pounds more than twice the weight of bag A
[1]$\textcolor{w h i t e}{\text{XXX}} B = 2 A + 3$
and if the total weight of both bags is 27 pounds
[2]$\textcolor{w h i t e}{\text{XXX}} A + B = 27$

Using [1] we can substitute $2 A + 3$ for $B$ in [2]
$A + B = 27 \textcolor{w h i t e}{\text{XX")rarrcolor(white)("XX}} A + 2 A + 3 = 27$

$\textcolor{w h i t e}{\text{XXXXXXXXXXXXXX}} 3 A + 3 = 27$

$\textcolor{w h i t e}{\text{XXXXXXXXXXXXXX}} 3 A = 24$

$\textcolor{w h i t e}{\text{XXXXXXXXXXXXXX}} A = 8$

Now substituting $8$ for $A$ in [2]
$A + B = 27 \textcolor{w h i t e}{\text{XX")rarrcolor(white)("XX}} 8 + B = 27$

$\textcolor{w h i t e}{\text{XXXXXXXXXXXXXX}} B = 19$