how do you solve this?

Question

Carlos and Ashley each improved their yards by planting daylilies and ivy.They bought their supplies from the same store.Carlos spent $230 on 14 daylilies and 10 pots of ivy.Ashley spent $118 on 10 daylilies and 2 pots of ivy.What is the cost of one daylily and the cost of one pot of ivy?

Answer 1

Let x be the cost of one day lily and y the cost of one pot of ivy.

 

Then,

 

230 = 14x + 10y

118 = 10x + 2y.

 

You must solve this system of equations. Here is one way to do it.

 

      230 = 14x + 10y    →    230 =  14x + 10y

-5 ( 118 = 10x + 2y )   →   -590 = -50x - 10y

 

The add together:   -360 = -36x  →  x = 10.

 

Plug this into one of the original equations to solve for y.

 

118 = 10(10) + 2y  →  2y = 18  →  y = 9.

 

They bought 10 day lilies and 9 ivy pots.

 

You can check this in the original problem statement.