Lesson 2.6 Skills Practice Name_________________________________________________________ Date__________________________
Hot Shirts Using Tables, Graphs, and Equations, Part 2
Vocabulary Define each term in your own words. 1. point of intersection
2. estimation
Problem Set Estimate each value of each expression. Then, calculate the exact value. 1. 750.25 1 225.50
2. 1.98 1 1.73
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975; 975.75
3. 25 3 101
4. 236 3 4
5. 146.9 2 92.5
6. 4261 2 2637
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Use the given information to complete each table and answer the question. 7. Job A will pay a $30,000 salary per year for the first year, with a $1200 raise each year. Job B will pay a $30,000 salary per year for the first year, with a 3% raise each year. Complete the table to show the annual salaries for the first 4 years, rounding each salary to the nearest dollar. In the fourth year, which job will pay the greater salary?
Year
Job A
Job B
1
$30,000
$30,000
2
$30,000 1 $1200 5 $31,200
$30,000 3 1.03 5 $30,900
3
$31,200 1 $1200 5 $32,400
$30,900 3 1.03 5 $31,827
4
$32,400 1 $1200 5 $33,600
$31,827 3 1.03 5 $32,782
Job A will pay a greater salary. 8. Job C is offering you a $40,000 salary for the first year, plus a one-time $3000 signing bonus. Each year, you get a $1500 raise. Job D is offering you $40,000 for the first year, and each year you get a 5% raise. Complete the table to show the annual salaries for the first 4 years. Which job will pay you more in total for all 4 years?
Year
Job C
Job D
2 3 4
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Name_________________________________________________________ Date__________________________ 9. You have a choice between two different investment options. You will invest $6000. Investment Plan A estimates that you will earn 6% of your account balance each year. Investment Plan B estimates that you will earn $370 each year. Complete the table to show the account balance for the first 4 years. After 4 years, which investment plan would have a greater account balance?
Year
Plan A
Plan B
1 2 3 4
10. You invest $5000 into each of two different accounts. In Account A, you will earn $50 each month. In Account B, you will earn 1% of your account balance at the end of each month. Complete the table to show the account balance for the first 4 months. After 4 months, which investment plan would have a greater account balance?
Month
Account A
Account B
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1 2 3 4
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11. On Big Country Dairy Farms, the average Holstein cow produces 40 pounds of milk daily in its first year of production and an additional 3 pounds of milk daily in each year after the first. The average Jersey cow produces 35 pounds of milk daily in its first year of production and an additional 4.5 pounds of milk daily in each year after the first. Complete the table to show each type of cows’ daily milk production for the first 5 years. After 5 years, which type of cow produces the most milk daily?
Year
Holstein’s Daily Milk Production (pounds)
Jersey’s Daily Milk Production (pounds)
1 2 3 4 5
12. Jerry puts a different type of fertilizer on each of his two pumpkin patches. A pumpkin from Patch A measures 13 ounces in week 1 and grows at a rate of 3.2 ounces per week. A pumpkin from Patch B measures 9 ounces in week 1 and grows at a rate of 3.6 ounces per week. Complete the table to show the growth for each pumpkin for 5 weeks. After 5 weeks, which pumpkin is the largest? Weight of the Patch A Pumpkin (ounces)
1 2 3 4
5
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Weight of the Patch B Pumpkin (ounces) © 2011 Carnegie Learning
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Name_________________________________________________________ Date__________________________ Use the given equations to answer each question. 13. Two catering companies host children’s sports banquets. Company A charges a fixed fee of $100 plus $3 per person. Company B charges a fixed fee of $75 plus $4 per person. The total charge for each company for any number of persons, p, can be calculated using the equations shown.
Company A: c 5 3p 1 100
Company B: c 5 4p 1 75
Which company would charge less to cater for 200 people? Company A: c 5 3(200) 1 100 5 700 Company B: c 5 4(200) 1 100 5 900 Company A would charge $200 less to cater for 200 people.
14. Lana is joining a gym. Get Fit charges $20 per month, plus a $99 initial set-up fee. Work It Out charges $30 per month, plus a $50 initial set-up fee. The equations show the total cost after any number of months, m. Get Fit: c 5 20m 1 99
Work It Out: c 5 30m 1 50
Which gym would cost less if you planned on being a member for 4 months?
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15. Theodore and Jeffrey are comparing their text messaging plans. Theodore’s cell phone company charges according to the equation c 5 5 1 0.10m. Jeffrey’s cell phone company charges according to the equation c 5 3 1 0.15m. Let c represent the total cost in dollars for m text messages sent and received. Which plan charges more to send or receive a total of 100 text messages?
16. Anthony and Lisa are both joining DVD rental programs. The cost of Anthony’s program per month can be represented by the equation c 5 10 1 1m. The cost of Lisa’s program per month can be represented by the equation c 5 5 1 2m. Let c represent the monthly cost if m DVDs are rented. Who would pay more if they each rented 7 movies in 1 month?
17. A coffee shop is ordering new coffee mugs. The total charges for The Mug Company are by c 5 25 1 0.50m. Let c represents the total cost of m mugs. If the coffee shop needs to order 100 mugs, which company should they order from?
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© 2011 Carnegie Learning
represented by the equation c 5 15 1 1.5m. The total charges for A Perfect Mug are represented
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Name_________________________________________________________ Date__________________________ 18. You are flying to visit some relatives in Boston. Budget Airline charges $150 for a round-trip ticket, plus an additional $0.20 per pound of luggage, which is represented by the equation c 5 150 1 0.20p. Let c represent the cost, and let p represent the pounds of luggage. Cheap Air charges $75 for a round-trip ticket, plus an additional $0.80 per pound of luggage, which is represented by the equation c 5 75 1 0.80p. If you are bringing 30 pounds of luggage, on which airline should you fly?
Use the given graph to answer each question. 19. You need to choose a shipping company. Ship Fast charges $2.00 per package plus $1.00 per pound. Speedy Delivery charges $3.00 per package plus $0.50 per pound. The graph of the equations that represent this situation is shown. For what package weight do both companies charge the same price? y 10 9
Shipping Cost (in dollars)
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8 Ship Fast
7 6
Speedy Delivery
5 4 3 2 1 1
2
3
4
5
6
7
8
9
10
x
Weight (in pounds)
A package weighing 2 pounds will cost the same to ship using either company.
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20. Tate is ordering flour for her bakery. Baker’s Supplies charges $0.30 per pound, plus a $10 delivery fee. Best Flour charges $0.80 per pound, but delivery is free. The graph of the equations that represent this situation is shown. For what weight of flour is the cost equal for both companies? y 30 27
Charge (in dollars)
24 21 18 15
Baker’s Supplies
12 9 6
Best Flour
3 3
6
12
9
15
18
21
24
27
30
x
Weight (in pounds)
21. Franklin is buying fabric. For the same material, Sew Right charges $4.00 per yard and an initial $5.00 convenience fee. Stitch Plus charges $6.00 per yard and a $2.00 convenience fee. The graph of the equations that represent this situation is shown. Which store should he buy the fabric from if he is buying 5 yards of material? y 30 27
Charge (in dollars)
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Stitch Plus
24
Sew Right
21 18 15 12 9 6 3 1
2
3
4
5
6
Length (in yards)
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8
9
10
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Name_________________________________________________________ Date__________________________ 22. An ice cream shop is choosing a milk delivery service. The Spotted Cow charges $2.80 per gallon plus a $2 delivery fee. Dairy Farms charges $2.10 per gallon plus a $10 delivery fee. The graph of the equations that represent this situation is shown. Who charges more to deliver 15 gallons of milk? y 50 45
Charge (in dollars)
40 35 30
Dairy Farms
25 20 15 Spotted Cow
10 5 3
6
9
12
15
18
21
24
27
30
x
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Gallons of Milk
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23. Aiko is trying to select a prepaid cell phone. The Texnel phone costs $15 per month plus $0.15 per minute. The Konia phone costs $25 per month plus $0.05 per minute. The graph of the equations that represent this situation is shown. If Aiko plans to talk an average of 150 minutes per month, which plan should she choose? 50
y
45 40
Cost of Plan ($)
35 30
Konia
25 Texnel
20 15 10 5 0
x 0
20
40
60
80 100 120 140 160 180 200 Minutes Used
24. A middle school principal is trying to select a publisher for the student handbook. Page One Publishing charges a start-up fee of $50 plus $0.75 per handbook printed. Page Two Publishing charges a start-up fee of $200 plus $0.25 per handbook printed. The graph of the equations that represent this situation is shown. Which publishing company should the principal choose if the school plans to print 200 handbooks? 500
y
450
© 2011 Carnegie Learning
400
Printing Cost ($)
350 300 Page Two
250 200
Page One
150 100 50
x
0 0
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50 100 150 200 250 300 350 400 450 500 Number of Handbooks Printed
