Model Equations
Two friends pooled the tickets they won from playing video games to get a prize that requires 800 tickets. If one friend won 130 more tickets than the other friend, how many tickets did each friend win?
2x + 8 = 20
x = 6
Equation: c/2 + 5 = 2
Possible solutions: − 6, 3, 6
− 6 makes the equation true.
8x > 56
x > 7
Ms. Moderelli charges her piano students $40 per lesson plus a semester recital fee of $55. How many lessons did Jerry take if he paid a total of $695 for lessons this semester?
Jerry took 16 lessons.
James and Kara spent $3043.51 to buy a new computer together. James spent $438.47 more than Kara. How much did James spend and how much did Kara spend?
Kara spent $1302.52 and James spent $1740.99
6m +7.2 = -2.8
m= -5/3
Equation: 2.1p − 7 = − 15.4
Possible solutions: − 4, − 2, 1
− 4 makes the equation true.
144 ≥ − 12x
− 12 ≤ x
The student council ordered 1000 pencils embossed with the school name to give to honor roll students. If they give each honor roll student two pencils and they have 840 pencils left after the first quarter, how many students are on the honor roll in the first quarter?
There are 80 students on the honor roll in the first quarter.
During the summer, Curran and AJ started their own business mowing lawns. Before starting any work, Curran spent $20to fill up the gas tank for the lawnmower. The boys agreed that each person would earn the same amount after Curran was reimbursed the money he spent for gas. After a week of work, the boys were paid a total of $177. Curran filled up the gas tank just once. How much did each boy earn?
Each boy will profit $78.50
2y − 4.25 = − 1.39
y = 1.43
Inequality: 10 ≥ 3n − 1/2
Possible solutions: − 2, 2, 9
− 2 and 2 make the inequality true.
− 17 < 3 − 5x
4 > x
Javier has a collection of 125 comic books. He gives each of his 3 friends the same number of comic books and keeps his favorite 38 comic books for himself. How many comic books did he give to each of his friends?
Javier gives each of his friends 29 comic books.
Cameron, Hannah, and Daniel are swimming laps to raise money for charity. Together, the three swimmers swam a total of 1875 laps. Hannah swam twice as many laps as Daniel. Cameron swam 125 fewer laps than Hannah. How many laps did each person swim?
Daniel swam 400 laps, Hannah swam 800 laps, and Cameron swam 675 laps.
− 7x − 11 = − 4.
x = -1
Inequality: − 2m − 10 ≤ 4
Possible solutions: − 7, − 2, 15
− 7, − 2, and 15 make the inequality true.
21 − 9x ≥ − 6
x ≤ 3
Vijay wants to keep the cost per person of his party under $15. The Party Place charges a flat fee of $250for an all-inclusive party. Let g represent the number of guests, including himself, he can invite
Vijay can invite 17 or more guests to his party.
You and your friends Kyra and Paolo decide to make some money during summer vacation by building and selling birdhouses. To get the business started, Kyra contributes $22, and Paolo contributes $18 to buy equipment and materials. You all agree that each person will earn the same amount of money after Kyra and Paolo get back what they invested. Your business earns a total of $280. How much does each person get at the end of the summer?
Each person will earn $80.
− 16 = 13 − g
g = 29
Equation: − 7.5 = h/9 − 4.9
Possible solutions: − 24.2, − 23.4, − 25.9
− 23.4 makes the equation true.
78 > 4x + 6
18 > x
There must be less than 36 people on one bus. There are already 17 people on the bus. Let p represent the additional number of people that can ride the bus.
Fewer than 19 additional people can ride on the bus.