Creating & Solving Equations

Rayshawn and Robert are both saving money for their summer vacations. They began saving at the same time. Rayshawn started with $10.25 and adds $5.15 to his savings every month. Robert did not have a starting amount but adds $10.25 to his savings every month. Which equation could be used to determine how many months, m, it will take before Rayshawn and Robert both have saved the same amount of money?

• 5.15m + 10.25 = 10.25m
• 10.25m + 5.15 = 10.25m
• 10.25m + 10.25 = 5.15m
• 10.25m – 5.15 = 10.25m

Renting boats on a lake costs $22 per hour plus a flat fee of $10 for insurance. If you paid $98 to rent the boat, how many hours did you rent the boat?
What is the correct equation to solve?

• 22 + 10h = 98
• 22 + 10 = 98h
• 98 + 10 = 22h
• 22h + 10 = 98

Solve for x:
2(3x + 4) + 2 = 4 + 3x

• 2
• -2/3
• 10
• -2

• x = 24
• x = 12
• x = 17.5
• x = 19.5

A​ town's population is 47,500. About 75 people move out of the town each month. Each​ month, 125 people on average move into town. A nearby town has a population of 50,250. It has no one moving in and an average of 200 people moving away every month. In about how many months will the populations of the towns be​ equal? Write an equation to model the situation. Then solve the equation and answer the question.

• 125m-75m+50,250=47,500-200m
• 75m-125m+ 50,250 = 47,500-200m
• 75m-125m+47,500 = 50,250-200m
• 125m-75m+47,500 = 50,250-200m

1. Which situation is best represented by the following equation?

45w + 123.95 = 753.95

• Erica paid $753.95 for dance classes. She paid a $45 registration fee and $123.95 for each week she was enrolled in the classes. What is w, the number of weeks Erica was enrolled in dance classes?

• Erica and her sister paid $753.95 for dance classes. Erica paid $123.95 for each week she was enrolled in the classes, and her sister paid $45 for each week she was enrolled in the classes. What is w, the number of weeks Erica and her sister were enrolled in dance classes?

• Erica paid $753.95 for dance classes. She paid a $123.95 registration fee and $45 for each week she was enrolled in the classes. What is w, the number of weeks Erica was enrolled in dance classes?

• Erica paid $753.95 for dance classes. She paid a $123.95 for each week she was enrolled in the classes after using a coupon that gave her $45 off the price per week. What is w, the number of weeks Erica was enrolled in dance classes?

A hockey season ticket holder pays $72.48 for all of her tickets plus $6 for a program each game. A second person pays $18.08 for a ticket to each game, but doesn’t buy programs.  Write an equation that shows when the two fans will pay the same amount.
In how many games will they have paid the same amount? 

• 18.08 + 6x = 72.48x;  6 games
• 72.48 + 6x = 18.08; 9 games
• 72.48 + 6x = 18.08x; 9 games
• 72.48 + 6x = 18.08x; 6 games

A hockey season ticket holder pays $72.48 for all of her tickets plus $6 for a program each game. A second person pays $18.08 for a ticket to each game, but doesn’t buy programs.

In how many games will they have paid the same amount?

• 6 games

• 7 games

• 8 games

• 9 games

Rayshawn and Robert are both saving money for their summer vacations. They began saving at the same time. Rayshawn started with $10.25 and adds $5.15 to his savings every month. Robert did not have a starting amount but adds $10.25 to his savings every month. Which equation could be used to determine how many months, m, it will take before Rayshawn and Robert both have saved the same amount of money?

• 5.15m + 10.25 = 10.25m
• 10.25m + 5.15 = 10.25m
• 10.25m + 10.25 = 5.15m
• 10.25m – 5.15 = 10.25m

Penelope is going to the carnival to ride the rides. It costs $20 to get into the carnival and ride tickets are $0.50 each. Write an equation that represents this scenario if she spends $35 in all.

• .50x + 20 = 35
• .50x = 35
• .50 + 20x = 35 
• .50x - 20 = 35