Two-Step Equations
3x + 4 = 10
x = 2
Sarah bought 3 notebooks and a pen for $11. The pen costs $2. How much does each notebook cost?
$3
5x - 4 = 3x + 6
x = 5
A gym charges a monthly fee of $30 plus $5 per class attended. Another gym charges $20 per month plus $10 per class. If a person attends the same number of classes at both gyms and the total cost is the same, how many classes did they attend?
2 classes
5(x - 3) + 1 = 3x + 8
x = 11
x = -7
A movie theater charges $8 per ticket and a $5 service fee per transaction. If the total cost for a group of friends was $37, how many tickets did they buy?
4 tickets
3x - 11 = -4x + 10
x = 3
A company offers two internet plans. Plan A costs $20 per month plus $3 per gigabyte of data used. Plan B costs $70 per month plus $1 per gigabyte. If a customer uses the same amount of data with both plans and the total cost is the same, how many gigabytes did they use?
25 gigabytes
3(x + 4) - 2 = 2x + 10
x = 0
-2(x + 3) = 14
x = -10
A gym membership costs $20 per month, and there is a one-time registration fee of $15. If someone paid a total of $135, how many months did they pay for?
6 months
8x - 7 = 2x + 9
x = 8/3
Two friends, Alex and Jamie, are saving money. Alex saves $25 per week, and Jamie saves $15 per week. Alex started with $60, and Jamie started with $140. After how many weeks will they have saved the same amount of money?
8 weeks
2(3x - 4) + 5 = 4x + 3(x - 2)
x = 3
(1/3)(6x - 9) = 5
x = 4
A landscaper charges $50 for a consultation and $30 per hour of work. If a client was charged a total of $200, how many hours did the landscaper work?
5 hours
2.5x + 3.4 = 1.5x + 7.4
x = 4
A car rental company offers two plans. Plan A charges $50 per day plus $0.20 per mile driven. Plan B charges $30 per day plus $0.30 per mile. If the total cost is the same for both plans, how many miles were driven?
200 miles
4(x + 2) - 3(x - 1) = 2x + 5
x = 6
0.4(x - 4) = 1.2
x = 7
A car rental company charges a flat fee of $25 plus $0.15 per mile driven. If a customer paid $40, how many miles did they drive?
100 miles
4.5x - 2.3 = 2.1x + 3.7
x = 2.5
A farmer is comparing two suppliers for fertilizer. Supplier A charges $0.75 per pound of fertilizer plus a delivery fee of $20. Supplier B charges $0.45 per pound of fertilizer plus a delivery fee of $35. For how many pounds of fertilizer will the cost for the two suppliers be the same?
50 pounds
3(2x + 1) - 4(x - 2) = 5(x + 1) + 2
x = 4/3