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Rewriting Equations with Variables
Overview
We can use what we know about solving for unknown numbers to rewrite equations involving variables. This can be much simpler than plugging in a set of numbers.
For example…
Rewrite the equation y + 3 = x to solve for y
We can use the relationship between addition and subtraction to solve for y
y + 3 = x
Move the 3 across the equal sign (=). When we do that, the addition operation
changes to subtraction.
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Rewrite the equation 6 ÷ y = x to solve for y
Answer
Use the relationship between multiplication and division
Rewrite the equation
Answer
Use the relationship between multiplication and division.
Rewrite the equation 3 + 2y = x to solve for y.
Answer
First use the relationship between addition and subtraction.
Then usethe relationship between multiplication and division.
Sarah is 3 times older than Jane. Jane is 2 years younger than Lars. If Lars is 12, how old is Sarah?
Answer
30 years old
Jane = Lars – 2 when Lars is 12. So, Jane = 12 – 2. Sarah = 3(Jane). So, Sarah = 3(10).
The baker places chocolate chip and sugar cookies into a box. There are 12 total cookies in the box. There are 2 more chocolate chip cookies than sugar cookies.
How many sugar cookies are there?
Answer
5
There are 12 total cookies. 2c + 2 = 12.
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