Question

You are in charge of snacks for a youth event. You send your cousin Norm who is a complete nerd to

the store to price some items for you. For some inexplicable reason instead of telling you the price
for each item, he gives you this information:
If you buy 3 bags of Reese's Peanut Butter Cups and 6 bags of York Peppermint Patties, it costs $48.
If you buy 4 bags of Reese's Peanut Butter Cups and 3 bags of York Peppermint Patties, it costs $51.
Figure out how much each single bag costs. (Do not enter a $, just the number)
Reese's Peanut Butter Cups:
York Peppermint Patties:

Answer 1

Reese's Peanut Butter Cups: 10.8

York Peppermint Patties: 2.6

Explanation:

Let Reese's Peanut Butter Cups be r and York Peppermint Patties y.

Step 1: Make equations.

1) If you buy 3 bags of Reese's Peanut Butter Cups and 6 bags of York Peppermint Patties, it costs $48.

`3r + 6y = 48`

2) If you buy 4 bags of Reese's Peanut Butter Cups and 3 bags of York Peppermint Patties, it costs $51.

`4r + 3y = 51`

Step 2: Solve the system of equations.

We have system of equations. I'll solve them by elimination.

`(1.) \text{ } 3r + 6y = 48\\(2.) \text{ } 4r + 3y = 51`

Multiply the second equation with 2 so we'll get 6y.

`(1.) \text{ } 3r + 6y = 48\\(2.) \text{ } 8r + 6y = 102`

Now let's subtract second equation from first and solve for r.

`3r - 8r + 6y - 6y = 48 - 102\\-5r = -54\\r = (-54)/(-5)\\r = \$10.8`

To get y let's substitute the value of r in first equation.

`3r + 6y = 48\\3 \cdot 10.8 + 6y = 48\\32.4 + 6y = 48\\6y = 15.6\\y = \$2.6`