What is the price of individual rocks and bags of lint?

Question

The local apothecary is selling rocks and bags of lint to anyone foolish enough to purchase them. Lloyd bought 5 rocks and 6 bags of lint for $190. Harry bought 6 rocks and 8 bags of lint for $244. What is the price of individual rocks and bags of lint? 

Answer 1

We need a system of equations. Let x = the price of a rock. Let y = the price of a bag of lint. We have:

 

5x + 6y = 190

 

6x + 8y = 244

 

We can solve this system by the Elimination Method

 

Let's multiply the top equation by 4, the bottom equation by 3, and then subtract

 

20x + 24y = 760

 

18x + 24y = 732

 

Subtracting gives us:

 

2x = 28

 

x = $14 = the price of a rock

 

You should now be able to find y, the price of a bag of lint, Julia