2.15.5 Practice

1. Which two inequalities could make up a system of inequalities that represents how many pennies and nickels that Jada could have? Select two inequalities.

• $p+n>20$
• $0.01p+0.05n>0.40$

For questions 2 – 4:

Determine if it is possible that Jada has each of the following combinations of coins. If so, explain or show how you know. If not, state which constraint—the amount of money or the number of coins—it does not meet.

2. 15 pennies and 5 nickels

3. 16 pennies and 2 nickels

4. 10 pennies and 8 nickels

5. A triathlon athlete swims at an average rate of 2.4 miles per hour, and bikes at an average rate of 16.1 miles per hour. At the end of one training session, she has swam and biked more than 20 miles in total.
   The inequality 2.4$s$ + 16.1$b$ > 20 and this graph represent the relationship between the hours of swimming, $s$, the hours of biking, $b$, and the total distance the athlete could have traveled in miles. ;

Mai said, "I'm not sure the graph is right. For example, the point (10,3) is in the shaded region, but it's not realistic for an athlete to swim for 10 hours and bike for 3 hours in a training session! I think triathlon athletes generally train for no more than 2 hours a day."

Which inequality represents Mai's last statement?

For questions 6 and 7, use the following situation and graph:

Elena is considering buying bracelets and necklaces as gifts for her friends. Bracelets, $b$,  cost $3, and necklaces, $n$, cost $5. She can spend no more than $30 on the gifts. Elena needs at least 7 gift items.
This graph represents the inequality $3b+5n\le 30$, which describes the cost constraint in this situation.

6. Let $b$ represent the number of bracelets and $n$ the number of necklaces.
   Which inequality represents the number of gift items that Elena needs?

7. Which of the following could be solutions to the system of inequalities? Select two answers.

• (8,5)
• (1,5)
• (7,1)
• (6,2)

8. A gardener is buying some topsoil and compost to fill his garden. His budget is $70. Topsoil costs $1.89 per cubic foot, and compost costs $4.59 per cubic foot.
   Select three statements or representations that correctly describe the gardener's constraints in this situation. Let $t$ represent the cubic feet of topsoil and $c$ the cubic feet of compost. ;

A: The combination of 7.5 cubic feet of topsoil and 12 cubic feet of compost is within the gardener's budget.

B: If the line on the graph represents the equation $1.89t$ + 4.59$c$ = 70, this graph represents the solutions to the gardener's budget constraint.

C: $1.89t$+4.59$c$≥70

D: The combination of 5 cubic feet of topsoil and 20 cubic feet of compost is within the gardener's budget.

E: $1.89t$+4.59$c$≤70

F: If the line on the graph represents the equation $1.89t$+4.59$c$=70, this graph represents the solutions to the gardener's budget constraint.

1. A
2. B
3. C
4. D
5. E
6. F

For questions 2 – 4:

Determine if it is possible that Jada has each of the following combinations of coins. If so, explain or show how you know. If not, state which constraint—the amount of money or the number of coins—it does not meet.

2. 15 pennies and 5 nickels

3. 16 pennies and 2 nickels

4. 10 pennies and 8 nickels

5. A triathlon athlete swims at an average rate of 2.4 miles per hour, and bikes at an average rate of 16.1 miles per hour. At the end of one training session, she has swam and biked more than 20 miles in total.
   The inequality 2.4$s$ + 16.1$b$ > 20 and this graph represent the relationship between the hours of swimming, $s$, the hours of biking, $b$, and the total distance the athlete could have traveled in miles. ;

Mai said, "I'm not sure the graph is right. For example, the point (10,3) is in the shaded region, but it's not realistic for an athlete to swim for 10 hours and bike for 3 hours in a training session! I think triathlon athletes generally train for no more than 2 hours a day."

Which inequality represents Mai's last statement?

6. Let $b$ represent the number of bracelets and $n$ the number of necklaces.
   Which inequality represents the number of gift items that Elena needs?

7. Which of the following could be solutions to the system of inequalities? Select two answers.

1. (8,5)
2. (1,5)
3. (7,1)
4. (6,2)

8. A gardener is buying some topsoil and compost to fill his garden. His budget is $70. Topsoil costs $1.89 per cubic foot, and compost costs $4.59 per cubic foot.
   Select three statements or representations that correctly describe the gardener's constraints in this situation. Let $t$ represent the cubic feet of topsoil and $c$ the cubic feet of compost. ;

A: The combination of 7.5 cubic feet of topsoil and 12 cubic feet of compost is within the gardener's budget.

B: If the line on the graph represents the equation $1.89t$ + 4.59$c$ = 70, this graph represents the solutions to the gardener's budget constraint.

C: $1.89t$+4.59$c$≥70

D: The combination of 5 cubic feet of topsoil and 20 cubic feet of compost is within the gardener's budget.

E: $1.89t$+4.59$c$≤70

F: If the line on the graph represents the equation $1.89t$+4.59$c$=70, this graph represents the solutions to the gardener's budget constraint.

1. A
2. B
3. C
4. D
5. E
6. F