1. Find a lower bound and an upper bound for the difference.
a) 8 - 4 < 8.76 - 3.95 < 9 - 3
4 < 8.76 - 3.95 < 6
b) < 9.4 - 3.2 <
< 9.4 - 3.2 <
c) < 8.57 - 2.19 <
< 8.57 - 2.19 <
d) < 6.38 - 0.57 <
< 6.38 - 0.57 <
2. Calculate the differences from Question 1.
a) b) c) d)
Are the actual differences between your upper and lower bounds? If not, find your mistake.
3. Hanna had $755.50 and spent $326.87.
a) Should she use an upper bound or a lower bound to estimate how much money she has left? Why?
b) Estimate how much money Hanna has left.
4. Glen is traveling from New York City to Philadelphia, then to Pittsburgh, then back to New York City. He estimates the amount of gas he needs, as shown on the map.
a) Use an upper or lower bound to estimate how much gas he should have for the trip.
b) Did you use an upper bound or a lower bound? Why?
New York
2.4 gallons
Philadelphia7.2 gallons
Pittsburgh 8.8 gallons
F-81Blackline Master—Ratios and Proportional Relationships —Teacher’s Guide for AP Book 7.1
1. Jane bought 3 T-shirts for $12 each and 3 sweaters for $28 each. Calculate how much money she spent, two ways. Make sure you get the same answer both ways.
3 × $12 + 3 × $28 3 × ($12 + $28)
= + = 3 ×
= =
2. Bilal bought 12 cans of juice for 87¢ each. He then sold them for 90¢ each.
a) Calculate Bilal’s profit.
selling price = 12 × 90¢
- buying price = 12 × 87¢
=
b) Calculate Bilal’s profit another way. Make sure you get the same answer both ways. Bilal’s profit = (Bilal’s profit from 1 can) × 12
= × 12
=
c) Which solution above matches the expression below? Write “part a)” or “part b)” beside the matching expression.
i) 12 × 90¢ - 12 × 87¢
ii) 12 × (90¢ - 87¢)
3. Do the problem mentally. Hint: Use the easier expression.
a) Karen buys CDs for $8 each and sells them for $13 each. How much profit would she make on 84 CDs?
b) Marco buys pens for $3 each and sells them for $3.50 each. How much profit would he make on 46 pens?
c) Mary buys bikes for $300 each and sells them for $320 each. How much profit would she make on 60 bikes?
d) Don gets $5 for each hour of cutting grass. If he cuts grass for 1 hour on Monday, 3 hours on Wednesday, and 7 hours on Saturday, how much money does he earn altogether?
4. Jennifer makes and sells pies for $8 each. She made 16 beef pies, 20 chicken pies, and 14 turkey pies. She paid $160 for the ingredients. If she worked 20 hours to make the pies, what was her profit per hour?
F-83Blackline Master—Ratios and Proportional Relationships —Teacher’s Guide for AP Book 7.1
Wendy’s salary decreased by 5%. Her new salary is 100% - 5% = 95% of her old salary.
So, new salary = 0.95 × old salary.
8. Tom’s salary decreased by 15%. His old salary was $45,000.
His new salary is × $45,000 = $ .
9. The value of a car decreased by 30%. The car was worth $25,000.
What is the car worth now? $25,000 × = $ .
10. A television set is on sale for 25% off. The regular price is $540.
The sale price is $540 × = $ .
11. In one year, there were 325 car accidents. The next year, the number of car accidents decreased by 8%. How many car accidents were there the next year?
12. When Kathy started running, she ran 5 km in 35 minutes. After two months of training, she decreased her time by 20%. How long does it take her to run 5 km now?
13. Zara’s salary increased by 8%. What can she multiply her old salary by to get her new salary?
14. Rick saw a haircut advertised for $40. He knows the sales tax where he lives is 7%. How much money should he bring to get his haircut?
15. A farm sold 15,000 apples and 12,000 pears in one year. In the next year, the number of apples sold increased by 5% and the number of pears sold decreased by 5%. Did the total number of apples and pears sold increase or decrease?
16. A computer costs $1,000 plus 15% tax. Which of these is the best deal?
A: A 15% discount on the $1,000 price, then a 15% tax on the sale price.
B: The store will pay the tax.
C: A 15% discount on the price after taxes are added.
