Name ______Date ______

LESSONS 1.1–1.4

Problem Solving Workshop: Mixed Problem Solving

For use with pages 2–26

1.Multi-Step Problem The kicker of a football team made 24 field goals and 43 extra points during a season.

a.The number n of points scored on field goals is given by 3f where f is the number of field goals made. How many points did the kicker score on field goals?

b.The point total is given by n + p where p is the number of extra points. Use your answer from part (a) to find the kicker’s point total.

2.Multi-Step Problem You go to an amusement park with a friend. You have a coupon for $2 off each admission ticket. The total cost (in dollars) of buying 6 game tickets at $1.50 each and 2 admission tickets at $14.95 each is given by the expression 6 • 1.50 + 2(14.95 – 2).

a.Find the total cost

b.You can spend $45. How much will you have left?

c.A hot dog costs $2.50, a slice of pizza costs $3, and a glass of iced tea costs $1.75. Do you have enough money left to buy 1 hot dog, 1 slice of pizza, and 2 glasses of iced tea?

3.Short Response You have to type a 600-word essay. Which expression would you evaluate to find the number of minutes it will take you to finish the essay typing at x a rate of x words per minute: 600x,

or ?

Justify your choice. Then find the x number of minutes it will take you to finish the essay typing at a rate of 30 words per minute.

4.Gridded Answer Screen-printed T-shirts cost $8 each. There is a $4 set-up charge for each order no matter how many T-shirts are ordered. Find the total cost (in dollars) if you order 10 T-shirts.

5.Short Response You burn 180 calories per hour walking and 260 calories per hour bicycling. You can exercise for a total of 8 hours this week and hope to burn 1800 calories. Let w be the number of hours you spend walking.

a.Write an inequality that describes the situation. Your inequality should involve only one variable, w.

b.You spend the same amount of time doing each exercise. Will you meet your goal? Explain.

6.Extended Response The table shows three students’ scores in a debate competition. A student’s final score is the sum of the points for content c and for delivery d.

Student / Content / Delivery
A / 25 / 40
B / 45 / 30
C / 30 / 25

a.Write a variable expression for a student’s final score.

b.Find each student’s final score.

c.You earn 35 points for content. At least how many points must you earn for delivery to have a higher score than students A, B, and C? Explain.

7.Open-Ended Describe a real-world situation you could model using the equation

x – 8 = 14. Use mental math to solve the equation. Explain what the solution means in the context of the situation.

8.Short Response A personal CD player costs $50 and CDs cost $12. Write an expression to represent the total cost of the CD player and n CDs. You buy a personal CD player and 3 CDs. Evaluate your expression to determine the total amount of money you spend.