Choosing Equations from Real World Problems

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

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.

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

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

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

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