Last month, a freelance coder billed clients for hours of front-end work and hours of back-end work. The equation
represents the total amount, in dollars, the coder earned. What is the best interpretation of the number in this context?
In an equation that adds earnings from two kinds of work, each coefficient (the number multiplying a letter) is a pay rate, and each letter counts hours. Match the coefficient to its own letter, then check the units: dollars per hour times hours gives dollars. Don’t mistake a pay rate for the hours worked or swap the work types.
Hints
- Hint 1
An hourly rate is dollars earned for one hour. Multiplying that rate by hours gives earnings in dollars. Which letter counts the back-end hours, and which number is multiplied by it?
- Hint 2
A coefficient is the number multiplying a letter. The letter tells you which kind of work the number belongs to. Does the coefficient describe one hour or all the hours worked?
Step-by-step
Match the coefficient to its hours
Step 1Identify the back-end earnings term
No Desmos needed. You’re interpreting the equation, not solving it. The problem calls the number of back-end hours, so the term represents earnings from back-end work. An hourly rate times a number of hours produces dollars, the unit of the total.
- Step 2
Interpret the number multiplying the hours
is the coefficient of : the number multiplied by the back-end hours. The coefficient gives dollars for one hour; the whole term gives dollars for all those hours. So the coder earned $55 per hour for back-end work, not hours of work. Choice C.