Linear Equations (One Variable)

Mr. Smith works as a salesman at a car dealership. He is paid a base salary of $1,300 each month, and he receives a commission of $150 for each vehicle he sells. If last month Smith earned $2,500, how many cars did he sell last month?
[Hint: Write a linear equation to model this information.]

• 8
• 10
• 6
• 12

Two trains are approaching each other on parallel tracks. One train is travelling at 50 mph and the other at 100 mph. If the trains are currently 900 miles apart, how many hours until they pass each other?
[Hint: Write a linear equation to model this information.]

• 6 hrs.
• 5 hrs.
• 7 hrs.
• 18 hrs.

It costs $80 per month to join a gym, but if you join you only have to pay $1 each time you want to use the pool. If you don't join the gym, you can still use the pool, but you have to pay $5 each time you do.
How many times per month would you have to use the pool before it would become worthwhile to join the gym?

• 20
• 13
• 14
• 19

Rhonda has a small workshop that makes roller skates. Her shop has fixed costs of $500 per day, plus it costs her $18 in materials to make each pair of skates
If she sells each pair of skates for $50, what is the minimum number of skates she must sell per day in order to make a profit?

• 16
• 15
• 7
• 8

The HS Chorus wants to take a field trip to Carnegie Hall. The Chorus already has $300 saved for the trip, but it needs to have $1,500 in order to go.
To raise money, the Chorus Boosters are selling sandwiches for $6.00 each. However, each sandwich costs $2.50 to make. How many sandwiches must the Boosters sell for the Chorus to be able to go on the field trip?

• 343
• 142
• 515
• 212

400 students came to a picnic. Some were freshmen and the rest were sophomores. Each freshman ate three cookies and each sophomore ate five cookies.
If a total of 1,760 cookies were eaten by students at this picnic, which equation below could help you find how many were freshmen?

• 3x + 5(400 − x) = 1,760
• 3(400 − x) + 5x = 1,760
• 3x + 5(x − 400) = 1,760
• 3(x  − 400) + 5x = 1,760

A math worksheet took Jeremy 1 hour and 15 minutes to complete. Each numerical problem took three minutes to complete and each word problem took five minutes to complete.
If there were 10 numerical problems on the worksheet, how many word problems were there?

• 9
• 6
• 7
• 8

Bree and Brittany are sisters. Bree has $700 in her savings account and is saving an additional $30 per week. Brittany has $1,500 in her savings account, but she is on a spending spree and is withdrawing $90 per week from her account.
How many weeks until Bree has more money saved than Brittany?

• 14
• 37
• 18
• 7

You have $120 budgeted to rent a moving truck for 2 days.  Each day is $39, plus $0.25 per mile.  How many miles can you drive the truck and stay within your budget?

• 170 miles
• 168 miles
• 150 miles
• 172 miles

The sum of two consecutive integers is 153.  Which equation could be used to find the first integer?

• 2n+1 = 153
• n + 1 = 153
• 2n = 153
• 2n + 2 = 153