Percent Increase, Percent Decrease and Percent Error: Grade 7 Math Test Answer Key – PDF Download

Question 1: Classify the change (2 points)

1. \(\frac{52-40}{40}=\frac{12}{40}=0.30\). A 30% increase.
2. \(\frac{60-75}{75}=\frac{-15}{75}=-0.20\). A 20% decrease.

Scoring: 1 point for each part: correct percent and the correct word (increase or decrease).

Question 2: New amounts (2 points)

1. \(0.15\times 120=18\); \(120+18=138\). $138.
2. \(0.25\times 64=16\); \(64-16=48\). 48 pounds.

Scoring: 1 point for each part. Award the point for a correct multiplier method (1.15 or 0.75) as well.

Question 3: Original price (2 points)

The sale price is \(100\%-40\%=60\%\) of the original: \(0.60\times \text{original}=54\), so \(\text{original}=54: 0.60=90\).

Check: \(40\%\) of $90 is $36 and \(90-36=54\). The original price was $90.

Scoring: 1 point for writing 54 as 60% of the original (or an equivalent equation); 1 point for the correct original price.

Question 4: Percent error (3 points)

1. \(|78.4-80|=1.6\) inches.
2. \(\frac{1.6}{80}=0.02=2\%\).
3. Board: \(\frac{|25.75-25|}{25}=\frac{0.75}{25}=0.03=3\%\). Since \(2\%\) is less than \(3\%\), the countertop measurement has the smaller percent error.

Scoring: 1 point for the error 1.6 in; 1 point for dividing by the actual length and getting 2%; 1 point for finding 3% and comparing correctly.

Question 5: Up then down (3 points)

1. \(1.25\times 48=60\). $60.
2. \(0.80\times 60=48\). $48.
3. The price is back at $48, a change of \(0\%\). The \(25\%\) was taken of $48 ($12) but the \(20\%\) was taken of the larger amount $60 (also $12), so the percents are of different amounts and cannot be added or subtracted.

Scoring: 1 point each for parts (a) and (b); 1 point for an explanation that the percents apply to different base amounts (or that the final price equals the starting price).

Question 6: Population (2 points)

Change: \(12{,}500-11{,}000=1{,}500\). \(\frac{1{,}500}{12{,}500}=0.12=12\%\).

A 12% decrease.

Scoring: 1 point for the change 1,500 divided by the original 12,500; 1 point for 12% decrease.

Question 7: Compare growth (3 points)

1. Plant A: \(\frac{10-8}{8}=\frac{2}{8}=25\%\). Plant B: \(\frac{24-20}{20}=\frac{4}{20}=20\%\).
2. \(25\%>20\%\), so Plant A grew by the greater percent, even though Plant B grew by more inches.

Scoring: 1 point for each correct percent; 1 point for the correct comparison.

Question 8: Discount and tax (3 points)

1. \(0.80\times \text{original}=44\), so \(\text{original}=44: 0.80=55\). $55.
2. Tax: \(0.07\times 44=3.08\). Total: \(44+3.08=47.08\). $47.08.
3. \(\frac{47.08-55}{55}=\frac{-7.92}{55}=-0.144\). A 14.4% decrease.

Scoring: 1 point for each part. In (c), accept a 14.4% decrease; do not penalize a rounding to 14% if the work is shown.

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