Finding Equations from Word Problems

The Harris County Fair costs $15.00 to get in and $2.50 per ride, while the Montgomery County Fair costs $10.00 to get in and $3.00 per ride. Which equation could be used to determine how many rides you would need to go on for both fairs to be of equal value?

• 15x + 2.5 = 10x + 3

• 15 + 2.5x = 10 + 3x

• 15-2.5x = 10

• 15 - 10 = 2.5x +3x

At Gamestop you can buy an Xbox One for $150.00 and each game to go with it would cost $24. Or, you can buy a Playstation 4 for $180.00 and each game for $20.00 Write an equation to determine how many games would need to be purchased for the cost to be equal.

• 150x + 24 = 180 + 20x

• 180 - 150 = 24x + 20x

• 150 + 24x = 180 + 20x

• 150 - 24x = 180 - 20x

Uber charges $8.00 to get into the car and $0.75 per mile. Lyft charges $6.00 to get into the car and $1.25 per mile. How many miles would your trip need to be for Uber and Lyft to cost you the same amount?

• 0.75 + 8x = 1.25 + 6x

• 6 + 0.75x = 8 + 1.25x

• 1.25x + 0.75x = 14

• 8 + 0.75x = 6 + 1.25x

Peppy Pets charges a flat fee of $15 plus $3 per hour to keep a dog during the day. Happy Hounds charges a flat fee of $21 plus $1 per hour. For how many hours is the total fee charged by the companies the same?

• 2 hours

• 3 hours

• 4 hours

• 5 hours

Kimberly takes the bus to work. The bus ride to work costs her $2.50 each time she rides it. She could buy a bus pass for a one-time fee of $15.00 and would then only pay $1.00 each time she rode the bus. Write and solve an equation to show when paying for these two options would cost the same amount.

Select the situation that could be modeled by: 120 + 25x = 45x.

• John bought a car radio for $120 and speakers for $25 each. Joe bought a radio for $45. They each paid the same. How much did they spend?

• George charges a flat fee of $120 to mow a lawn plus $25 per hour. Greg charges $45 an hour to mow a lawn. After how many hours do they make the same amount?

• Lisa pays $120 for each purse she buys plus an additional $25 each to have them personalized. Lauren pays $45 for each purse she buys. How many purses must they buy for the amount they spent to be the same?

• Winnie bought a family meal with 8 burgers and 4 fries. Wilson bought a family meal with 12 burgers and 3 fries. If they each paid the same amount, how much did they spend?

• Team A runs 8 drills that are 4 minutes each. Team B runs 12 drills that are 3 minutes each. Which team practices longer?

• The basketball team currently has 8 players and is growing by 4 players each month. The volleyball team has 12 players and is growing by 3 players each month. After how many months will they have the same number of players?

• The basketball team currently has 4 players and is growing by 8 players each month. The volleyball team has 3 players and is growing by 12 players each month. After how many months will they have the same number of players?

Joe's Canoes charges an initial fee of $20 plus $4 an hour. Callie's Canoes charges a flat rate of $14 an hour. Choose the equation that would find the number of hours that the total for both places would charge the same.

• 4x + 20 = 14x

• 24x = 14x

• 4x - 20 = 14x

• 20 + 4x = 14

Ms. Cronin has 400 followers on Instagram and is gaining 75 followers each day. Ms. Willis has 1,000 followers on Instagram, but is losing 25 followers a day. After how many days will Ms. Cronin and Ms. Willis have the same number of followers?instaginstinstagram

• 4 days

• 14 days

• 12 days

• 6 days

Shelby has $155 in savings, and her boyfriend George has $230. Shelby is saving $10 each week, and George is spending $15 each week. After how many weeks will Shelby and George have the same amount?

• 3 days

• 25 days

• 5 days

• 7 days