Algebra 2 chapter 3.1

Question

A shop has one-pound bags of peanuts for $2 and three-pound bags of peanuts for $5.50. If you buy five bags and spend $17, how many bags of each size did you buy?

Answer 1

This is a system of two linear equations. Let x and y represent the number of one-pound and three-pound bags respectively. Then the number of bags are given by

x + y = 5

and the cost of the five bags (or the total amount you spent) is

2x + 5.5y = 17

Solve for x in the first equation (x = 5 - y), and substitute that into the second one

2(5-y) + 5.5y = 17

10 - 2y + 5.5y = 17

3.5y = 7

y = 2

And

x = 5 - y = 3.

Hope that helps.