Testinar Grade 7 math

Applying Proportional Reasoning to Real-World Problems

Students will build Grade 7 mastery of applying proportional reasoning to real-world problems using models, equations, and test-style reasoning.

CH01-06 Ratios and Proportional Relationships
Name
Date
Score
____ / 8
Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

  1. A fruit stand sells apples and oranges in the ratio \(12:8\). In simplest form, what is the ratio?

    1. \(6:4\)
    2. \(4:3\)
    3. \(2:3\)
    4. \(3:2\)

  2. A beverage mix uses \(1\) part juice concentrate for every \(5\) parts water. Complete the ratio table: What is \(x + y\)?

    Applying Proportional Reasoning to Real-World Problems visual for G7-C01-T06-Q002
    1. \(17\)
    2. \(20\)
    3. \(22\)
    4. \(25\)

  3. A recipe for lemonade uses \(2\) cups lemon juice and \(8\) cups water. Which statement is true?

    1. The ratio of lemon to water is \(1:3\)
    2. The ratio of lemon to water is \(1:4\)
    3. For every \(3\) cups of lemon, there are \(12\) cups of water
    4. The ratio of water to lemon is \(3:1\)

  4. A recipe for cookies uses a flour-to-butter ratio of \(8:3\). Which of the following quantities represents the same ratio?

    1. \(12\) cups flour, \(4\) cups butter
    2. \(24\) cups flour, \(8\) cups butter
    3. \(8\) cups flour, \(6\) cups butter
    4. \(16\) cups flour, \(6\) cups butter

  5. A salt water solution uses a ratio of \(2\) parts salt to \(9\) parts water. If you use \(18\) cups of water, how many cups of salt are needed?

    1. \(2\) cups
    2. \(3\) cups
    3. \(4\) cups
    4. \(6\) cups

  6. A store sells \(6\) notebooks for $15. What is the unit price (cost per notebook)?

    1. $1.50
    2. $5.00
    3. $4.00
    4. $2.50

  7. A cyclist travels at an average speed of \(15\) miles per hour. How far does the cyclist travel in \(2.5\) hours?

    1. \(27.5\) miles
    2. \(30\) miles
    3. \(35\) miles
    4. \(37.5\) miles

  8. A sedan travels \(210\) miles on \(10\) gallons of gas. An SUV travels \(180\) miles on \(12\) gallons of gas. Which vehicle has the better fuel efficiency (miles per gallon)?

    1. Cannot be determined
    2. The SUV (\(15\) mpg vs.~\(21\) mpg)
    3. They are equal
    4. The sedan (\(21\) mpg vs.~\(15\) mpg)
Teacher and parent reference

Answer key and explanations

  1. D. \(3:2\)

    Divide both \(12\) and \(8\) by their GCD, which is \(4\): \(12 \div 4 = 3\) and \(8 \div 4 = 2\). So the simplest form is \(3:2\).

  2. C. \(22\)

    Ratio is \(1:5\). When juice \(= 3\): water \(= 3 \times 5 = 15\), so \(y = 15\). When water \(= 35\): juice \(= 35 \div 5 = 7\), so \(x = 7\). Thus \(x + y = 7 + 15 = 22\).

  3. B. The ratio of lemon to water is \(1:4\)

    Ratio \(2:8\) simplifies to \(1:4\) (divide both by 2). Option D incorrectly states \(3:1\) instead of \(4:1\).

  4. D. \(16\) cups flour, \(6\) cups butter

    Ratio \(8:3\) scaled by \(2\) gives \(16:6\). Check: \(\frac{16}{6} = \frac{8}{3}\) (divide numerator and denominator by 2). Option B reduces to \(3:1\). Option C reduces to \(4:3\) (not \(8:3\)).

  5. C. \(4\) cups

    Ratio \(2:9\). If water \(= 18\), then \(\frac{2}{9} = \frac{x}{18}\), so \(x = 2 \times 2 = 4\) cups salt.

  6. D. $2.50

    Unit price \(= $15 \div 6 = $2.50\) per notebook.

  7. D. \(37.5\) miles

    Distance \(= \text{speed} \times \text{time} = 15 \times 2.5 = 37.5\) miles.

  8. D. The sedan (\(21\) mpg vs.~\(15\) mpg)

    Sedan: \(210 \div 10 = 21\) mpg. SUV: \(180 \div 12 = 15\) mpg. The sedan has better fuel efficiency.

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