Solution:

Convert to decimal and multiply: $0.15 \times 200 = 30$

Answer: $30$

SAT Tip: 15% = 0.15 (move decimal two places left)

Solution:

Use percent change formula: $\text{Percent Change} = \frac{100 - 80}{80} \times 100\%$

$= \frac{20}{80} \times 100\%$

$= 0.25 \times 100\% = 25\%$

Answer: $25\%$ increase

Solution:

Use percent change formula: $\text{Percent Change} = \frac{100 - 80}{80} \times 100\%$

$= \frac{20}{80} \times 100\%$

$= 0.25 \times 100\% = 25\%$

Answer: $25\%$ increase

Solution:

Total ratio parts: $3 + 5 = 8$

Girls represent $\frac{5}{8}$ of total: $\frac{5}{8} \times 40 = 25$

Answer: 25 girls

Check: Boys = $\frac{3}{8}(40) = 15$; Total = $15 + 25 = 40$ ✓

Solution:

Total ratio parts: $3 + 5 = 8$

Girls represent $\frac{5}{8}$ of total: $\frac{5}{8} \times 40 = 25$

Answer: 25 girls

Check: Boys = $\frac{3}{8}(40) = 15$; Total = $15 + 25 = 40$ ✓

Step 1: Total parts = $3 + 5 = 8$

Step 2: Each part = $\frac{24}{8} = 3$ students

Step 3: Girls = $5 \times 3 = 15$

Check: Boys = $3 \times 3 = 9$. Total = $9 + 15 = 24$ ✓

Answer: 15 girls

Step 1: Total parts = $3 + 5 = 8$

Step 2: Each part = $\frac{24}{8} = 3$ students

Step 3: Girls = $5 \times 3 = 15$

Check: Boys = $3 \times 3 = 9$. Total = $9 + 15 = 24$ ✓

Answer: 15 girls

Step 1: Total parts = $3 + 5 = 8$

Step 2: Each part = $\frac{24}{8} = 3$ students

Step 3: Girls = $5 \times 3 = 15$

Check: Boys = $3 \times 3 = 9$. Total = $9 + 15 = 24$ ✓

Answer: 15 girls

Step 1: Apply the 20% discount using a multiplier: $\$45 \times 0.80 = \$36$

Step 2: Apply 8% sales tax: $\$36 \times 1.08 = \$38.88$

One-step method: \45 \times 0.80 \times 1.08 = $38.88$

Answer: $38.88

SAT Tip: Use multipliers for efficiency. Discount of 20% → multiply by 0.80. Tax of 8% → multiply by 1.08.

Step 1: Apply the 20% discount using a multiplier: $\$45 \times 0.80 = \$36$

Step 2: Apply 8% sales tax: $\$36 \times 1.08 = \$38.88$

One-step method: \45 \times 0.80 \times 1.08 = $38.88$

Answer: $38.88

SAT Tip: Use multipliers for efficiency. Discount of 20% → multiply by 0.80. Tax of 8% → multiply by 1.08.

Step 1: Apply the 20% discount using a multiplier: $\$45 \times 0.80 = \$36$

Step 2: Apply 8% sales tax: $\$36 \times 1.08 = \$38.88$

One-step method: \45 \times 0.80 \times 1.08 = $38.88$

Answer: $38.88

SAT Tip: Use multipliers for efficiency. Discount of 20% → multiply by 0.80. Tax of 8% → multiply by 1.08.

Use the percent change formula: $\text{Percent Change} = \frac{\text{New} - \text{Original}}{\text{Original}} \times 100$

$= \frac{15{,}600 - 12{,}000}{12{,}000} \times 100$

$= \frac{3{,}600}{12{,}000} \times 100$

$= 0.30 \times 100 = 30\%$

Answer: 30% increase

Key: Always divide by the ORIGINAL value, not the new value.

Use the percent change formula: $\text{Percent Change} = \frac{\text{New} - \text{Original}}{\text{Original}} \times 100$

$= \frac{15{,}600 - 12{,}000}{12{,}000} \times 100$

$= \frac{3{,}600}{12{,}000} \times 100$

$= 0.30 \times 100 = 30\%$

Answer: 30% increase

Key: Always divide by the ORIGINAL value, not the new value.

Use the percent change formula: $\text{Percent Change} = \frac{\text{New} - \text{Original}}{\text{Original}} \times 100$

$= \frac{15{,}600 - 12{,}000}{12{,}000} \times 100$

$= \frac{3{,}600}{12{,}000} \times 100$

$= 0.30 \times 100 = 30\%$

Answer: 30% increase

Key: Always divide by the ORIGINAL value, not the new value.

Step 1: A 15% discount means the customer pays 85% of the original price. $\text{Original} \times 0.85 = 680$

Step 2: Solve for the original price: $\text{Original} = \frac{680}{0.85} = \$800$

Check: $800 \times 0.85 = 680$ ✓

Answer: $800

Common mistake: Don't calculate 15% of 680 and add it. That gives $680 + 102 = 782$, which is WRONG because the 15% should be based on the original price, not the sale price.

Step 1: A 15% discount means the customer pays 85% of the original price. $\text{Original} \times 0.85 = 680$

Step 2: Solve for the original price: $\text{Original} = \frac{680}{0.85} = \$800$

Check: $800 \times 0.85 = 680$ ✓

Answer: $800

Common mistake: Don't calculate 15% of 680 and add it. That gives $680 + 102 = 782$, which is WRONG because the 15% should be based on the original price, not the sale price.

Step 1: A 15% discount means the customer pays 85% of the original price. $\text{Original} \times 0.85 = 680$

Step 2: Solve for the original price: $\text{Original} = \frac{680}{0.85} = \$800$

Check: $800 \times 0.85 = 680$ ✓

Answer: $800

Common mistake: Don't calculate 15% of 680 and add it. That gives $680 + 102 = 782$, which is WRONG because the 15% should be based on the original price, not the sale price.

Step 1: After year 1 (10% increase): $\$1{,}000 \times 1.10 = \$1{,}100$

Step 2: After year 2 (10% decrease): $\$1{,}100 \times 0.90 = \$990$

Step 3: Net percent change: $\frac{990 - 1000}{1000} \times 100 = -1\%$

Answer: $990 after two years; net change is a 1% DECREASE.

Key Insight: A 10% increase followed by a 10% decrease does NOT return to the original value! The multiplier is $1.10 \times 0.90 = 0.99$, which is a 1% net decrease. This is because the 10% decrease is applied to a LARGER number.

Step 1: After year 1 (10% increase): $\$1{,}000 \times 1.10 = \$1{,}100$

Step 2: After year 2 (10% decrease): $\$1{,}100 \times 0.90 = \$990$

Step 3: Net percent change: $\frac{990 - 1000}{1000} \times 100 = -1\%$

Answer: $990 after two years; net change is a 1% DECREASE.

Key Insight: A 10% increase followed by a 10% decrease does NOT return to the original value! The multiplier is $1.10 \times 0.90 = 0.99$, which is a 1% net decrease. This is because the 10% decrease is applied to a LARGER number.

Step 1: After year 1 (10% increase): $\$1{,}000 \times 1.10 = \$1{,}100$

Step 2: After year 2 (10% decrease): $\$1{,}100 \times 0.90 = \$990$

Step 3: Net percent change: $\frac{990 - 1000}{1000} \times 100 = -1\%$

Answer: $990 after two years; net change is a 1% DECREASE.

Key Insight: A 10% increase followed by a 10% decrease does NOT return to the original value! The multiplier is $1.10 \times 0.90 = 0.99$, which is a 1% net decrease. This is because the 10% decrease is applied to a LARGER number.