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Word Problems – System of Equations

To solve a word problem using a system of equations, it is important to;
– Identify what we don’t know
– Declare variables
– Use sentences to create equations

An example on how to do this:

Mary and Jose each bought plants from the same store. Mary spent $188 on 7 cherry trees and 11 rose bushes. Jose spent $236 on 13 cherry trees and 11 rose bushes. Find the cost of one cherry tree and the cost of one rose bush.

Cost of a cherry tree:  x
Cost of a rose bush:  y
7 cherry trees and 11 rose bushes = $188
 7x + 11y = 188
 13x + 11y = 236

 7x + 11y = 188
 \underline {-13x - 11y = -236 }

The y-values cancel each other out, so now you are left with only x-values and real numbers.

 -6x = -48
 x = 8

Then, you plug in your x-value into an original equation in order to find the y-value.

 7x + 11y = 188
 7(8) + 11y = 188
 56 + 11y = 188
 11y = 132
 y = 12

Cost of a cherry tree: $8
Cost of a rose bush: $12

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