Question

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?

Answer 1

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`