MINI LESSON
Modeling Linear Equations
A linear equation can model relationships described in words.
Start by defining the variable and then translate each phrase carefully.
Phrases like 'sum,' 'more than,' 'less than,' and 'times' help determine the operations.
A correct equation matches the quantities and the story context.
Question 1
The sum of Tim's age and Jack's age is 44. Tim's age is 4 less than 7 times Jack's age, \(x\). An equation that could be used to model this scenario is
Question 2
Josie has \(\$2.30\) in dimes and quarters. She has two more dimes than quarters. Which equation below can be used to determine \(x\), the number of quarters she has?
Question 3
At Adelynn's first birthday party, each guest brought \(\$1\) in coins for her piggy bank. Guests brought nickels, dimes, and quarters for a total of \(\$28\). There were twice as many dimes as nickels and 12 more quarters than nickels. Which equation could be used to determine the number of nickels, \(x\), that her guests brought to her party?