Percent Increase and Decrease Worksheet | Fun and Engaging 7th ... - Free Printable

Problem Analysis and Solution

The provided worksheet focuses on percent increase and decrease. Let's solve the problems step by step.

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#### Section A: Percent Increase and Decrease

##### Left Table: Increase the following amounts by...
We need to calculate the new values after increasing the given amounts by 10%, 25%, and 1%.

1. $20
- 10% increase: $20 + (10\% \times 20) = 20 + 0.1 \times 20 = 20 + 2 = \$22$
- 25% increase: $20 + (25\% \times 20) = 20 + 0.25 \times 20 = 20 + 5 = \$25$
- 1% increase: $20 + (1\% \times 20) = 20 + 0.01 \times 20 = 20 + 0.2 = \$20.20$

2. $16
- 10% increase: $16 + (10\% \times 16) = 16 + 0.1 \times 16 = 16 + 1.6 = \$17.60$
- 25% increase: $16 + (25\% \times 16) = 16 + 0.25 \times 16 = 16 + 4 = \$20$
- 1% increase: $16 + (1\% \times 16) = 16 + 0.01 \times 16 = 16 + 0.16 = \$16.16$

3. $32
- 10% increase: $32 + (10\% \times 32) = 32 + 0.1 \times 32 = 32 + 3.2 = \$35.20$
- 25% increase: $32 + (25\% \times 32) = 32 + 0.25 \times 32 = 32 + 8 = \$40$
- 1% increase: $32 + (1\% \times 32) = 32 + 0.01 \times 32 = 32 + 0.32 = \$32.32$

4. $60
- 10% increase: $60 + (10\% \times 60) = 60 + 0.1 \times 60 = 60 + 6 = \$66$
- 25% increase: $60 + (25\% \times 60) = 60 + 0.25 \times 60 = 60 + 15 = \$75$
- 1% increase: $60 + (1\% \times 60) = 60 + 0.01 \times 60 = 60 + 0.6 = \$60.60$

5. $400
- 10% increase: $400 + (10\% \times 400) = 400 + 0.1 \times 400 = 400 + 40 = \$440$
- 25% increase: $400 + (25\% \times 400) = 400 + 0.25 \times 400 = 400 + 100 = \$500$
- 1% increase: $400 + (1\% \times 400) = 400 + 0.01 \times 400 = 400 + 4 = \$404$

6. $2,700
- 10% increase: $2,700 + (10\% \times 2,700) = 2,700 + 0.1 \times 2,700 = 2,700 + 270 = \$2,970$
- 25% increase: $2,700 + (25\% \times 2,700) = 2,700 + 0.25 \times 2,700 = 2,700 + 675 = \$3,375$
- 1% increase: $2,700 + (1\% \times 2,700) = 2,700 + 0.01 \times 2,700 = 2,700 + 27 = \$2,727$

7. $18,500
- 10% increase: $18,500 + (10\% \times 18,500) = 18,500 + 0.1 \times 18,500 = 18,500 + 1,850 = \$20,350$
- 25% increase: $18,500 + (25\% \times 18,500) = 18,500 + 0.25 \times 18,500 = 18,500 + 4,625 = \$23,125$
- 1% increase: $18,500 + (1\% \times 18,500) = 18,500 + 0.01 \times 18,500 = 18,500 + 185 = \$18,685$

##### Right Table: Decrease the following amounts by...
We need to calculate the new values after decreasing the given amounts by 50%, 20%, and 2.5%.

1. $30
- 50% decrease: $30 - (50\% \times 30) = 30 - 0.5 \times 30 = 30 - 15 = \$15$
- 20% decrease: $30 - (20\% \times 30) = 30 - 0.2 \times 30 = 30 - 6 = \$24$
- 2.5% decrease: $30 - (2.5\% \times 30) = 30 - 0.025 \times 30 = 30 - 0.75 = \$29.25$

2. $14
- 50% decrease: $14 - (50\% \times 14) = 14 - 0.5 \times 14 = 14 - 7 = \$7$
- 20% decrease: $14 - (20\% \times 14) = 14 - 0.2 \times 14 = 14 - 2.8 = \$11.20$
- 2.5% decrease: $14 - (2.5\% \times 14) = 14 - 0.025 \times 14 = 14 - 0.35 = \$13.65$

3. $22
- 50% decrease: $22 - (50\% \times 22) = 22 - 0.5 \times 22 = 22 - 11 = \$11$
- 20% decrease: $22 - (20\% \times 22) = 22 - 0.2 \times 22 = 22 - 4.4 = \$17.60$
- 2.5% decrease: $22 - (2.5\% \times 22) = 22 - 0.025 \times 22 = 22 - 0.55 = \$21.45$

4. $70
- 50% decrease: $70 - (50\% \times 70) = 70 - 0.5 \times 70 = 70 - 35 = \$35$
- 20% decrease: $70 - (20\% \times 70) = 70 - 0.2 \times 70 = 70 - 14 = \$56$
- 2.5% decrease: $70 - (2.5\% \times 70) = 70 - 0.025 \times 70 = 70 - 1.75 = \$68.25$

5. $800
- 50% decrease: $800 - (50\% \times 800) = 800 - 0.5 \times 800 = 800 - 400 = \$400$
- 20% decrease: $800 - (20\% \times 800) = 800 - 0.2 \times 800 = 800 - 160 = \$640$
- 2.5% decrease: $800 - (2.5\% \times 800) = 800 - 0.025 \times 800 = 800 - 20 = \$780$

6. $3,400
- 50% decrease: $3,400 - (50\% \times 3,400) = 3,400 - 0.5 \times 3,400 = 3,400 - 1,700 = \$1,700$
- 20% decrease: $3,400 - (20\% \times 3,400) = 3,400 - 0.2 \times 3,400 = 3,400 - 680 = \$2,720$
- 2.5% decrease: $3,400 - (2.5\% \times 3,400) = 3,400 - 0.025 \times 3,400 = 3,400 - 85 = \$3,315$

7. $26,200
- 50% decrease: $26,200 - (50\% \times 26,200) = 26,200 - 0.5 \times 26,200 = 26,200 - 13,100 = \$13,100$
- 20% decrease: $26,200 - (20\% \times 26,200) = 26,200 - 0.2 \times 26,200 = 26,200 - 5,240 = \$20,960$
- 2.5% decrease: $26,200 - (2.5\% \times 26,200) = 26,200 - 0.025 \times 26,200 = 26,200 - 655 = \$25,545$

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#### Section B: Word Problems

##### 1) DVD costing $30 reduced by 15%
- New price: $30 - (15\% \times 30) = 30 - 0.15 \times 30 = 30 - 4.5 = \$25.50$

##### 2) House costing $400,000 increased by 10%
- New price: $400,000 + (10\% \times 400,000) = 400,000 + 0.1 \times 400,000 = 400,000 + 40,000 = \$440,000$

##### 3) Population of 900 increased by 12%
- New population: $900 + (12\% \times 900) = 900 + 0.12 \times 900 = 900 + 108 = 1,008$

##### 4) Car bought for $7,500 sold with 30% profit
- Selling price: $7,500 + (30\% \times 7,500) = 7,500 + 0.3 \times 7,500 = 7,500 + 2,250 = \$9,750$

##### 5) Shopkeeper's expenses
- a) Total spent in 2005 (5% sales tax)
- Glass door cost: $1,500 (excluding tax)
- Sales tax on glass door: $1,500 \times 5\% = 1,500 \times 0.05 = \$75$
- Total cost of glass door: $1,500 + 75 = \$1,575$
- New counter cost: $120 (including tax)
- Total spent: $1,575 + 120 = \$1,695$

- b) Additional cost if sales tax increased to 20%
- Sales tax on glass door (20%): $1,500 \times 20\% = 1,500 \times 0.2 = \$300$
- Total cost of glass door (20%): $1,500 + 300 = \$1,800$
- Additional cost: $1,800 - 1,575 = \$225$

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Final Answers

#### Section A
- Increase Table
- $20$: $22$, $25$, $20.20$
- $16$: $17.60$, $20$, $16.16$
- $32$: $35.20$, $40$, $32.32$
- $60$: $66$, $75$, $60.60$
- $400$: $440$, $500$, $404$
- $2,700$: $2,970$, $3,375$, $2,727$
- $18,500$: $20,350$, $23,125$, $18,685$

- Decrease Table
- $30$: $15$, $24$, $29.25$
- $14$: $7$, $11.20$, $13.65$
- $22$: $11$, $17.60$, $21.45$
- $70$: $35$, $56$, $68.25$
- $800$: $400$, $640$, $780$
- $3,400$: $1,700$, $2,720$, $3,315$
- $26,200$: $13,100$, $20,960$, $25,545$

#### Section B
1. $\boxed{25.50}$
2. $\boxed{440000}$
3. $\boxed{1008}$
4. $\boxed{9750}$
5. a) $\boxed{1695}$, b) $\boxed{225}$

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These are the detailed solutions and final answers for the worksheet.