Solving by Using Modeling
Writing equations from Word Problems
Solving Word Problems
100
Use the model shown to solve for the variable.
4
100
Eddie compared prices of two auto-rental agencies for the use of a mid-size auto for one week. Right Price Auto charged a flat fee of $386 plus 20¢ per mile driven. EconoCar charged a flat fee of $344 plus 35¢ per mile driven. Which equation should he use to determine the distance in miles, m, that would make the total charges of both auto-rental agencies equal?
386 + .20m = 344 + .35m
100
Ronald rents a car from Cheap Rent-a-Car for $25 plus $0.05 per mile. Dixon rents a car from Great Cars for $40 plus $0.03 per mile. How many miles must they both drive for their rental fees to be the same?
750
200
An equation is represented by the model below.
What is the value of x that makes the equation true?
200
Jack and Tim are racing remote-controlled cars. Jack’s car travels 3.5 feet per second, while Tim’s car travels 5.25 feet per second. Because Jack’s car is slower, Tim gave Jack a 10-foot head start. Which inequality could be used to determine after how many seconds, s, Tim’s car will be ahead of Jack’s car?
5.25s > 3.5s + 10
200
Buffalo Bart’s Endless Wings charges $5.60 for sides and a drink, and then $0.40 per chicken wing. The Spicy Chicken charges $10 for sides and a drink, and then $0.20 per chicken wing. About how many chicken wings must be purchased so that the total cost at Buffalo Bart’s Endless Wings and The Spicy Chicken is the same?
22
300
The model represents an equation.
What value of x makes the equation true?
2.25
300
Jim received notice from his employer that the equation to calculate his salary was changing. Currently he makes $300 per week plus 4% commission on sales. The new equation will be $450 plus 2% commission on sales. Write and equation that shows the amount in sales he will need for his salary to be the same.
450 + 0.02s = 300 + 0.04s
300
Ryan’s membership to a video game club is $50 a year and $3 per game rented. If Ryan spent $296 in one year, how many games did he rent?
82
400
The algebra tiles shown below model an equation.
What equation best represents the model?
2n – 7 = 3n – 3
400
Sara makes hair clips and sells them for $6 each. Her total costs are $50 plus $2.80 per clip. How many clips, x, does she have to sell to make a profit?
6x > 50 + 2.80x
400
Mr. Bucci goes to the grocery store and purchases 17 bags of raisins and a $2.97 jar of peanut butter. His total cost was $34.76. What was the cost for a bag of raisins?
Each bag of raisins cost $1.87
500
Maggie and Melanie own a local business together and are about to give gifts to their employees to celebrate being open 5 years. They have purchased small gifts that are identical for their front office staff. For their personal assistants, they have each purchased larger gifts.
- Maggie purchased 4 large gifts and 2 small gifts.
- Melanie purchased 1 large gift and 20 small gifts.
- Each small gift cost $10.
- Each large gift costs the same amount of money.
A. Draw a model and an algebraic representation to reflect this situation if Maggie and Melanie both spent the same amount.
B. How much did they spend on the large gift?
$60
500
Write an equation that could be used to find the length of the side of the square below.
2x + 8 = 4x
500
Katie just bought a new car and really wants to keep it looking good. There are two car washes near her apartment. The first place, called Shiny charges a monthly fee of $9.99 then $5.00 per car wash. If Katie plans to wash her cars 5 time this month then what is the final cost?
9.99 + 5(x)
9.99 + 5(5)
$34.99