Independent practice worksheet on solving word problems that lead to inequalities.
A math worksheet titled "Word Problems Leading to Inequalities - Independent Practice Worksheet" with ten problems involving real-life scenarios and inequalities.
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Step-by-step solution for: Word Problems Leading To Inequalities Independent Practice ...
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Show Answer Key & Explanations
Step-by-step solution for: Word Problems Leading To Inequalities Independent Practice ...
It seems you've provided a list of word problems related to inequalities and their solutions on a number line. Since the image itself is not visible, I'll solve each problem step by step based on the text you've provided.
---
Statement: Julia has $80. She wants to purchase a nail paint set for $16 and earrings. She spends the rest of the money on earrings. Each pair of earrings costs $5. Write an inequality for the number of pairs of earrings she can purchase.
Solution:
1. Let \( x \) be the number of pairs of earrings Julia can purchase.
2. The cost of the nail paint set is $16.
3. The cost of \( x \) pairs of earrings is \( 5x \).
4. Julia has $80 in total. After buying the nail paint set, she has \( 80 - 16 = 64 \) dollars left.
5. The inequality representing the situation is:
\[
5x \leq 64
\]
6. Solve for \( x \):
\[
x \leq \frac{64}{5} = 12.8
\]
Since \( x \) must be a whole number (you can't buy a fraction of a pair of earrings), the maximum number of pairs she can buy is 12.
7. The inequality is:
\[
x \leq 12
\]
Graph on a Number Line:
- Draw a closed circle at 12 (since \( x \) can be 12).
- Shade the region to the left of 12, including 12.
---
Solution:
1. Start with the inequality:
\[
0.7x + 2 > 5.5
\]
2. Subtract 2 from both sides:
\[
0.7x > 3.5
\]
3. Divide both sides by 0.7:
\[
x > 5
\]
Graph on a Number Line:
- Draw an open circle at 5 (since \( x \) cannot be 5).
- Shade the region to the right of 5.
---
Statement: Caroline goes to the market with $20. She buys two pies for $20 and spends the rest of the money on bananas. Each banana costs $0.6. Write an inequality for the number of bananas she can purchase.
Solution:
1. Let \( y \) be the number of bananas Caroline can purchase.
2. The cost of two pies is $20.
3. Since she spends all her money on the pies, she has $0 left for bananas.
4. The inequality representing the situation is:
\[
0.6y \leq 0
\]
5. Solve for \( y \):
\[
y \leq 0
\]
Since \( y \) represents the number of bananas, and it cannot be negative, the only solution is \( y = 0 \).
Graph on a Number Line:
- Draw a closed circle at 0.
- There is no shading since \( y \) can only be 0.
---
Solution:
1. Start with the inequality:
\[
1.2x + 8 \geq 9.6
\]
2. Subtract 8 from both sides:
\[
1.2x \geq 1.6
\]
3. Divide both sides by 1.2:
\[
x \geq \frac{1.6}{1.2} = \frac{4}{3} \approx 1.33
\]
Graph on a Number Line:
- Draw a closed circle at \( \frac{4}{3} \) (or approximately 1.33).
- Shade the region to the right of \( \frac{4}{3} \).
---
Statement: Billy goes to the store with $90. He wants to purchase a leather jacket for $45, a belt for $10, and jeans. Each pair of jeans costs $35. Write an inequality for the number of jeans he can purchase.
Solution:
1. Let \( z \) be the number of pairs of jeans Billy can purchase.
2. The cost of the leather jacket is $45.
3. The cost of the belt is $10.
4. The total cost of the jacket and belt is \( 45 + 10 = 55 \).
5. Billy has $90 in total. After buying the jacket and belt, he has \( 90 - 55 = 35 \) dollars left.
6. The cost of \( z \) pairs of jeans is \( 35z \).
7. The inequality representing the situation is:
\[
35z \leq 35
\]
8. Solve for \( z \):
\[
z \leq 1
\]
Graph on a Number Line:
- Draw a closed circle at 1.
- Shade the region to the left of 1, including 1.
---
Solution:
1. Start with the inequality:
\[
2.6x + 8 > 2 - 12x
\]
2. Add \( 12x \) to both sides:
\[
2.6x + 12x + 8 > 2
\]
\[
14.6x + 8 > 2
\]
3. Subtract 8 from both sides:
\[
14.6x > -6
\]
4. Divide both sides by 14.6:
\[
x > \frac{-6}{14.6} \approx -0.411
\]
Graph on a Number Line:
- Draw an open circle at approximately \(-0.411\).
- Shade the region to the right of \(-0.411\).
---
Statement: Rebecca bought one gold fish ($32) and one star fish ($12). She spends the rest of her money on guppy fish. She starts with $80. Each guppy costs $8. Write an inequality for the number of guppies she can purchase.
Solution:
1. Let \( g \) be the number of guppies Rebecca can purchase.
2. The cost of the gold fish is $32.
3. The cost of the star fish is $12.
4. The total cost of the gold fish and star fish is \( 32 + 12 = 44 \).
5. Rebecca has $80 in total. After buying the gold fish and star fish, she has \( 80 - 44 = 36 \) dollars left.
6. The cost of \( g \) guppies is \( 8g \).
7. The inequality representing the situation is:
\[
8g \leq 36
\]
8. Solve for \( g \):
\[
g \leq \frac{36}{8} = 4.5
\]
Since \( g \) must be a whole number, the maximum number of guppies she can buy is 4.
9. The inequality is:
\[
g \leq 4
\]
Graph on a Number Line:
- Draw a closed circle at 4.
- Shade the region to the left of 4, including 4.
---
Statement: Erin has $50. She wants to purchase a cell phone ($50) and spend the rest of her money on CDs. Each CD costs $8. Write an inequality for the number of music CDs she can purchase.
Solution:
1. Let \( c \) be the number of CDs Erin can purchase.
2. The cost of the cell phone is $50.
3. Since Erin spends all her money on the cell phone, she has $0 left for CDs.
4. The inequality representing the situation is:
\[
8c \leq 0
\]
5. Solve for \( c \):
\[
c \leq 0
\]
Since \( c \) represents the number of CDs, and it cannot be negative, the only solution is \( c = 0 \).
Graph on a Number Line:
- Draw a closed circle at 0.
- There is no shading since \( c \) can only be 0.
---
Solution:
1. Start with the inequality:
\[
2.3x + 5 < -13
\]
2. Subtract 5 from both sides:
\[
2.3x < -18
\]
3. Divide both sides by 2.3:
\[
x < \frac{-18}{2.3} \approx -7.826
\]
Graph on a Number Line:
- Draw an open circle at approximately \(-7.826\).
- Shade the region to the left of \(-7.826\).
---
Solution:
1. Start with the inequality:
\[
0.4x - 4 < 2.4
\]
2. Add 4 to both sides:
\[
0.4x < 6.4
\]
3. Divide both sides by 0.4:
\[
x < \frac{6.4}{0.4} = 16
\]
Graph on a Number Line:
- Draw an open circle at 16.
- Shade the region to the left of 16.
---
1. \( x \leq 12 \)
2. \( x > 5 \)
3. \( y \leq 0 \)
4. \( x \geq \frac{4}{3} \)
5. \( z \leq 1 \)
6. \( x > -\frac{6}{14.6} \approx -0.411 \)
7. \( g \leq 4 \)
8. \( c \leq 0 \)
9. \( x < -\frac{18}{2.3} \approx -7.826 \)
10. \( x < 16 \)
\boxed{x \leq 12, x > 5, y \leq 0, x \geq \frac{4}{3}, z \leq 1, x > -0.411, g \leq 4, c \leq 0, x < -7.826, x < 16}
---
Problem 1: Julia's Nail Polish Set
Statement: Julia has $80. She wants to purchase a nail paint set for $16 and earrings. She spends the rest of the money on earrings. Each pair of earrings costs $5. Write an inequality for the number of pairs of earrings she can purchase.
Solution:
1. Let \( x \) be the number of pairs of earrings Julia can purchase.
2. The cost of the nail paint set is $16.
3. The cost of \( x \) pairs of earrings is \( 5x \).
4. Julia has $80 in total. After buying the nail paint set, she has \( 80 - 16 = 64 \) dollars left.
5. The inequality representing the situation is:
\[
5x \leq 64
\]
6. Solve for \( x \):
\[
x \leq \frac{64}{5} = 12.8
\]
Since \( x \) must be a whole number (you can't buy a fraction of a pair of earrings), the maximum number of pairs she can buy is 12.
7. The inequality is:
\[
x \leq 12
\]
Graph on a Number Line:
- Draw a closed circle at 12 (since \( x \) can be 12).
- Shade the region to the left of 12, including 12.
---
Problem 2: Solve \( 0.7x + 2 > 5.5 \)
Solution:
1. Start with the inequality:
\[
0.7x + 2 > 5.5
\]
2. Subtract 2 from both sides:
\[
0.7x > 3.5
\]
3. Divide both sides by 0.7:
\[
x > 5
\]
Graph on a Number Line:
- Draw an open circle at 5 (since \( x \) cannot be 5).
- Shade the region to the right of 5.
---
Problem 3: Caroline's Bananas
Statement: Caroline goes to the market with $20. She buys two pies for $20 and spends the rest of the money on bananas. Each banana costs $0.6. Write an inequality for the number of bananas she can purchase.
Solution:
1. Let \( y \) be the number of bananas Caroline can purchase.
2. The cost of two pies is $20.
3. Since she spends all her money on the pies, she has $0 left for bananas.
4. The inequality representing the situation is:
\[
0.6y \leq 0
\]
5. Solve for \( y \):
\[
y \leq 0
\]
Since \( y \) represents the number of bananas, and it cannot be negative, the only solution is \( y = 0 \).
Graph on a Number Line:
- Draw a closed circle at 0.
- There is no shading since \( y \) can only be 0.
---
Problem 4: Solve \( 1.2x + 8 \geq 9.6 \)
Solution:
1. Start with the inequality:
\[
1.2x + 8 \geq 9.6
\]
2. Subtract 8 from both sides:
\[
1.2x \geq 1.6
\]
3. Divide both sides by 1.2:
\[
x \geq \frac{1.6}{1.2} = \frac{4}{3} \approx 1.33
\]
Graph on a Number Line:
- Draw a closed circle at \( \frac{4}{3} \) (or approximately 1.33).
- Shade the region to the right of \( \frac{4}{3} \).
---
Problem 5: Billy's Jackets
Statement: Billy goes to the store with $90. He wants to purchase a leather jacket for $45, a belt for $10, and jeans. Each pair of jeans costs $35. Write an inequality for the number of jeans he can purchase.
Solution:
1. Let \( z \) be the number of pairs of jeans Billy can purchase.
2. The cost of the leather jacket is $45.
3. The cost of the belt is $10.
4. The total cost of the jacket and belt is \( 45 + 10 = 55 \).
5. Billy has $90 in total. After buying the jacket and belt, he has \( 90 - 55 = 35 \) dollars left.
6. The cost of \( z \) pairs of jeans is \( 35z \).
7. The inequality representing the situation is:
\[
35z \leq 35
\]
8. Solve for \( z \):
\[
z \leq 1
\]
Graph on a Number Line:
- Draw a closed circle at 1.
- Shade the region to the left of 1, including 1.
---
Problem 6: Solve \( 2.6x + 8 > 2 - 12x \)
Solution:
1. Start with the inequality:
\[
2.6x + 8 > 2 - 12x
\]
2. Add \( 12x \) to both sides:
\[
2.6x + 12x + 8 > 2
\]
\[
14.6x + 8 > 2
\]
3. Subtract 8 from both sides:
\[
14.6x > -6
\]
4. Divide both sides by 14.6:
\[
x > \frac{-6}{14.6} \approx -0.411
\]
Graph on a Number Line:
- Draw an open circle at approximately \(-0.411\).
- Shade the region to the right of \(-0.411\).
---
Problem 7: Rebecca's Fish
Statement: Rebecca bought one gold fish ($32) and one star fish ($12). She spends the rest of her money on guppy fish. She starts with $80. Each guppy costs $8. Write an inequality for the number of guppies she can purchase.
Solution:
1. Let \( g \) be the number of guppies Rebecca can purchase.
2. The cost of the gold fish is $32.
3. The cost of the star fish is $12.
4. The total cost of the gold fish and star fish is \( 32 + 12 = 44 \).
5. Rebecca has $80 in total. After buying the gold fish and star fish, she has \( 80 - 44 = 36 \) dollars left.
6. The cost of \( g \) guppies is \( 8g \).
7. The inequality representing the situation is:
\[
8g \leq 36
\]
8. Solve for \( g \):
\[
g \leq \frac{36}{8} = 4.5
\]
Since \( g \) must be a whole number, the maximum number of guppies she can buy is 4.
9. The inequality is:
\[
g \leq 4
\]
Graph on a Number Line:
- Draw a closed circle at 4.
- Shade the region to the left of 4, including 4.
---
Problem 8: Erin's CDs
Statement: Erin has $50. She wants to purchase a cell phone ($50) and spend the rest of her money on CDs. Each CD costs $8. Write an inequality for the number of music CDs she can purchase.
Solution:
1. Let \( c \) be the number of CDs Erin can purchase.
2. The cost of the cell phone is $50.
3. Since Erin spends all her money on the cell phone, she has $0 left for CDs.
4. The inequality representing the situation is:
\[
8c \leq 0
\]
5. Solve for \( c \):
\[
c \leq 0
\]
Since \( c \) represents the number of CDs, and it cannot be negative, the only solution is \( c = 0 \).
Graph on a Number Line:
- Draw a closed circle at 0.
- There is no shading since \( c \) can only be 0.
---
Problem 9: Solve \( 2.3x + 5 < -13 \)
Solution:
1. Start with the inequality:
\[
2.3x + 5 < -13
\]
2. Subtract 5 from both sides:
\[
2.3x < -18
\]
3. Divide both sides by 2.3:
\[
x < \frac{-18}{2.3} \approx -7.826
\]
Graph on a Number Line:
- Draw an open circle at approximately \(-7.826\).
- Shade the region to the left of \(-7.826\).
---
Problem 10: Solve \( 0.4x - 4 < 2.4 \)
Solution:
1. Start with the inequality:
\[
0.4x - 4 < 2.4
\]
2. Add 4 to both sides:
\[
0.4x < 6.4
\]
3. Divide both sides by 0.4:
\[
x < \frac{6.4}{0.4} = 16
\]
Graph on a Number Line:
- Draw an open circle at 16.
- Shade the region to the left of 16.
---
Final Answers:
1. \( x \leq 12 \)
2. \( x > 5 \)
3. \( y \leq 0 \)
4. \( x \geq \frac{4}{3} \)
5. \( z \leq 1 \)
6. \( x > -\frac{6}{14.6} \approx -0.411 \)
7. \( g \leq 4 \)
8. \( c \leq 0 \)
9. \( x < -\frac{18}{2.3} \approx -7.826 \)
10. \( x < 16 \)
\boxed{x \leq 12, x > 5, y \leq 0, x \geq \frac{4}{3}, z \leq 1, x > -0.411, g \leq 4, c \leq 0, x < -7.826, x < 16}
Parent Tip: Review the logic above to help your child master the concept of inequalities word problems worksheet.
![Two-Step Inequality (Word Problems) Worksheets [PDF] (7.EE.B.4.B ...](/images2/inequalities-word-problems-worksheet/inequalities-word-problems-worksheet-18.png)
