Substitution Worksheet With Answer Key - Waynesville R-Vi School District Page 24
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386-2 Substitution
If a + b = 7, then by subtracting a from each side, b = 7 a. In step 2, Guillermo substituted a + 7 for b and he
should have substituted 7 a.
Cara solved the first equation for a by subtracting b from each side. So, a = 7 b. She then substituted for a in the
second equation.
She should have then substituted the solution for b into the first equation to find the value of a which is the variable
for the number of apples.
The number of apples should be 4.
Therefore, neither Guillermo nor Cara is correct. Guillermo substituted incorrectly for b. Cara solved correctly for a,
but misinterpreted the pounds of apples bought.
A local charity has 60 volunteers. The ratio of boys to girls is 7:5. Find the number of
boy and the number of girl volunteers.
Let g represent the number of girls and b represent the number of boys. Since the total number of volunteers is 60,
one equation is g + b = 60. A second equation can be written as
, since the ratio of boys to girls is 7:5. To find
Page 24
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the number of boys and girls, solve the system of equations.
First, solve the first equation for g
b from each side to get g = 60
b. Then, substitute 60
b into the
second equation for g.
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