Word Problems

STARTUP
1.) 14 + 3n = 8n – 3(n – 4)
2.) x – (2x + 20) = 12

• The Keywords PER and EACH tell us to MULTIPLY
• Examples:
• Jill drives 35 miles PER hour we would MULTIPLY that by the number of HOURS to find the distance in miles d=35H
• Jamie has already spent $15 she is buying teeshirts that cost $12EACH. Write an equation for the Total she spent.
– Teeshirts $12 EACH (we would multiply by the number of teeshirts purchased,n) 12n
– She also apent $15 already we would ADD that on 12n+15
– This would be the Total she spent T=12n+15

Worksheet 2.2 Write an equation that models the situation. Then, solve the problem.
25) A rectangular trampoline has an area of 187 square feet. The length of the trampoline is 17 feet.
What is its width?

26) The van used to transport patients to and from rehabilitation facility is equipped with a wheelchair lift. The maximum lifting capacity for the lift is 300 pounds. The wheelchairs used by the facility weigh 55 pounds each. What is the maximum weight of a wheelchair occupant who can use the lift?

27) A dance academy charges $24 per class and a one-time registration fee of $15. A student paid a total of $687 to the academy. Find the number of classes the student took.

28) Jenny has a job that pays her $8 per hour plus tips (t). Jenny worked for 4 hours on Monday and made $65 in all. How much money did Jenny make in tips on Monday?

Jeremy mowed several lawns to earn money for camp.
After he paid $17 for gas, he had $75 leftover to pay towards camp. Write and solve an equation to find how much money Jeremy earned mowing lawns.

Chip earns a base salary of $500 per month as a salesman. In addition to the salary, he earns $90 per product that he sells. If his goal is to earn $5000 per month, how many products does he need to sell?

General admission tickets to the fair cost $3.50 per person. Ride passes cost an additional $3.50 per person. Parking costs $6 for the family. The total costs for ride passes and parking was $51. How many people in the family attended the fair?

Shirley is going to have the exterior of her home painted. Tim’s Painting charges $250 plus $14 per hour.
Colorful Paints charges $22 per hour. How many hours would the job need to take for Tim’s Painting to be the better deal?

Josie’s goal is to run 25 miles each week. This week she has already run the distances shown in the table
She wants to have one day of rest and to spread out the remaining miles evenly over the rest of the week.
Which equation can she use to find how many miles m per day she must run?
Mon. Tues. Wed. Thur. Fri. Sat. Sun.
2 2.5
4.5
?
?
?
?

The cost c of purchasing r roses from Sandra’s
Delivery Service is given by the equation c = 4r + 10. If Luke has $50 to spend on roses, how many roses can he buy?

Dave plans to rent a 14-foot truck for a two-day move. At Thrifty
Truck Rental, Dave can rent a truck for $25.95 per day plus $0.75 per mile driven. At Rent-a-Truck, Dave can rent a truck for $50 per day plus $0.50 per mile driven. After how many miles driven is the rental cost of the truck the same at both agencies?

At a vacation resort, you can water ski for $45 per hour plus a $15 fee for equipment rental.
Your bill came to $240. How many hours did you water ski?

You work 6 hours on Saturday and 5 hours on Sunday. You also receive a $25 bonus.
You earn $121.25 for the week. How much did you earn per hour?

Online concert tickets cost $57 each, plus a service charge of $7.50 per ticket. The Web site also charges a transaction fee of $9.99 for the purchase. You paid
$396.99. How many tickets did you buy?

Shirley is going to have the exterior of her home painted. Tim’s Painting charges $275 plus $12 per hour.
Colorful Paints charges $28 per hour. How many hours would the job need to take for Tim’s Painting to be the better deal?