Integrated Math 1 / Unit 2: Equations and Inequalities
2.5 Modeling with Equations
Notes
To model a situation, define a variable, translate the words into an equation, solve, and interpret the answer with units.
- "Is" or "equals" becomes $=$. "Per" often means multiply. "Decreased by" means subtract.
- A flat fee is a constant; a charge per item multiplies the variable.
- Example: a plan costs $20 plus $5 per GB. If the bill is $55, then $20 + 5g = 55$, so $g = 7$ GB.
- Check that the answer makes sense in the story.
Practice
A phone plan costs $20 plus $5 per gigabyte. A bill is $55. How many gigabytes were used?
$20 + 5g = 55 \Rightarrow 5g = 35 \Rightarrow g = 7$.
A rectangle's length is 2 more than 3 times its width. Its perimeter is 44. What is the width?
Length is $3w + 2$. Then $2(w + 3w + 2) = 44$, so $8w + 4 = 44$ and $w = 5$.
Which equation models "three times a number decreased by 4 equals 20"?
"Three times a number" is $3n$, and "decreased by 4" subtracts 4.
Ready for more? Take the Unit 2 test.