Question 7·Easy·Linear Equations in One Variable
Lena earns $12 per hour babysitting and receives a one-time $8 bonus for completing a first-aid course.
If she babysits for hours in one week, what expression represents, in dollars, the total amount Lena earns that week in terms of ?
For word problems that ask for an expression in terms of a variable, first identify which amounts depend on the variable (like "per hour" or "per item") and multiply those rates by the variable. Then identify any fixed amounts (bonuses, starting fees, discounts) and add or subtract them as separate terms. As a quick check, plug in an easy value (like 1 or 2) for the variable and see which answer choice matches the situation’s total.
Hints
Separate the two kinds of pay
Ask yourself: which part of Lena’s pay changes with the number of hours, and which part is the same no matter how many hours she works?
Translate "per hour" into math
"Per hour" means you multiply the hourly rate by the number of hours . Which number should be multiplied by ?
Combine the changing part and the fixed part
Once you have the expression for the hourly pay, how do you include the one-time $8 bonus to get her total earnings?
Desmos Guide
Compute a specific example from the story
Pick a simple number of hours, such as . According to the description, Lena earns $12 for each of the 2 hours plus an $8 bonus. In Desmos, type 12*2 + 8 and note the total dollar amount for 2 hours.
Test each answer choice with the same number of hours
In Desmos, type each option using :
- For A, type
8*2 + 12 - For B, type
12*2 + 8 - For C, type
20*2 - For D, type
8*(2 + 12)Compare each result to the total you found in Step 1 from the word problem. The expression that gives the same total is the correct one.
Step-by-step Explanation
Identify what depends on hours and what does not
Lena earns $12 for each hour she babysits, so this part of her pay changes when changes. She also receives a one-time $8 bonus, which stays the same no matter how many hours she works.
Write an expression for the hourly earnings
Because she earns $12 for each hour and she works hours, multiply the hourly rate by the number of hours to get the variable part of her earnings: .
Add the fixed bonus to get the total
To find her total earnings, combine the money that depends on hours and the fixed bonus:
- Hourly earnings:
- One-time bonus: $8
Add these together to get the total weekly earnings in terms of :
So the correct expression is .