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?

1 Answer
Feb 6, 2017

Answer:

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]#color(white)("XXX")B=2A+3#
and if the total weight of both bags is 27 pounds
[2]#color(white)("XXX")A+B=27#

Using [1] we can substitute #2A+3# for #B# in [2]
#A+B=27color(white)("XX")rarrcolor(white)("XX")A+2A+3=27#

#color(white)("XXXXXXXXXXXXXX")3A+3=27#

#color(white)("XXXXXXXXXXXXXX")3A=24#

#color(white)("XXXXXXXXXXXXXX")A=8#

Now substituting #8# for #A# in [2]
#A+B=27color(white)("XX")rarrcolor(white)("XX")8+B=27#

#color(white)("XXXXXXXXXXXXXX")B=19#