SBAC Math Grade 7 Ratios and Proportions 2 — Questions and Answers

Question 1: A store sells 3 apples for $1.50. At this rate, how much do 7 apples cost?

$2.50
$3.00
$3.50 (Correct answer)
$4.00

Correct answer: $3.50

Unit rate: $1.50 ÷ 3 = $0.50 per apple. 7 × $0.50 = $3.50.

This is a unit rate problem. First find the cost per single apple, then scale up to 7 apples. Unit rate: $1.50 ÷ 3 apples = $0.50 per apple Cost of 7 apples: 7 × $0.50 = $3.50 You can also set up a proportion: 3/1.50 = 7/x. Cross multiply: 3x = 7 × 1.50 = 10.50. Divide: x = 10.50/3 = 3.50. Or use equivalent ratios: 3 apples for $1.50. To get 7 apples, you need 2 full sets of 3 (6 apples for $3.00) plus 1 more apple at $0.50, totaling 7 apples for $3.50. Finding unit rates (cost per item, miles per hour, etc.) is a fundamental skill. Once you know the unit rate, you can easily scale to any quantity by multiplying. Unit rates appear constantly in everyday life: price comparisons, speed calculations, cooking ratios.

Question 2: A scale drawing uses 1 inch = 12 feet. If a room is 3.5 inches on the drawing, what is its actual length?

15.5 feet
36 feet
42 feet (Correct answer)
3.5 feet

Correct answer: 42 feet

Multiply the drawing measurement by the scale factor: 3.5 inches × 12 feet/inch = 42 feet.

A scale drawing uses a ratio to represent real-world measurements. The scale 1 inch = 12 feet means that every inch on the drawing represents 12 feet in real life. To find the actual length: 3.5 inches × 12 feet/inch = 42 feet. The units work out: inches cancel, leaving feet. 3.5 × 12 = 42. You can also set up a proportion: 1 inch/12 feet = 3.5 inches/x feet Cross multiply: x = 3.5 × 12 = 42 feet Scale drawings appear in maps, architectural plans, engineering diagrams, and models. The scale factor is the ratio of the drawing measurement to the actual measurement. Here the scale factor is 1:12 (or 1/12), meaning everything in the drawing is 1/12 the actual size. Units are critical in scale problems. Always write out the units to make sure the conversion makes sense. '3.5 inches × 12 feet per inch' — the inches cancel, giving an answer in feet.

Question 3: A car travels 150 miles in 2.5 hours. What is its average speed in miles per hour?

40 mph
50 mph
55 mph
60 mph (Correct answer)

Correct answer: 60 mph

Speed = distance ÷ time = 150 miles ÷ 2.5 hours = 60 miles per hour.

Speed is a rate that compares distance to time. The formula is: Speed = Distance ÷ Time. Speed = 150 miles ÷ 2.5 hours = 60 miles per hour To divide by 2.5, multiply both numerator and denominator by 2: 300/5 = 60. Check: If the car travels 60 mph for 2.5 hours: 60 × 2.5 = 60 × 2 + 60 × 0.5 = 120 + 30 = 150 miles. ✓ The three variables in rate problems (distance, speed, time) are related by: Distance = Speed × Time. If you know any two, you can find the third. This is one of the most common and practical applications of proportional reasoning. The unit 'miles per hour' (mph) is a ratio — it compares miles to hours. 60 mph means 60 miles for every 1 hour of travel. This unit rate thinking helps solve many real-world problems.

Question 4: What is 35% of 80?

24
25
28 (Correct answer)
35

Correct answer: 28

35% of 80 = 0.35 × 80 = 28. Or: 35/100 × 80 = 2800/100 = 28.

To find a percent of a number, convert the percent to a decimal and multiply. 35% = 35/100 = 0.35 0.35 × 80 = 28 You can also use mental math: 10% of 80 = 8. 35% = 30% + 5% = (3 × 8) + (half of 8) = 24 + 4 = 28. Or: 35% = 1/4 + 10% = 20 + 8 = 28. (Since 25% of 80 = 20 and 10% of 80 = 8, then 35% = 25% + 10% = 20 + 8 = 28.) Percent problems come in three types: (1) Find the percent of a number [this problem], (2) Find what percent one number is of another, (3) Find the whole when given a part and the percent. For type 1, always convert percent to decimal and multiply. For types 2 and 3, set up a proportion: part/whole = percent/100.

Question 5: Is the relationship between x and y proportional? x: 2, 4, 6, 8 and y: 5, 10, 15, 20.

No, because the numbers are not equal
Yes, because the ratio y/x is constant at 5/2 (Correct answer)
No, because y increases faster than x
Yes, because both sequences increase by the same amount

Correct answer: Yes, because the ratio y/x is constant at 5/2

The ratios y/x are 5/2, 10/4, 15/6, 20/8 — all equal to 5/2 = 2.5. Constant ratio = proportional relationship.

A proportional relationship is one where the ratio between the two quantities is always the same. This constant ratio is called the constant of proportionality (often written as k). Check each pair: y/x 5/2 = 2.5 10/4 = 2.5 15/6 = 2.5 20/8 = 2.5 Since all ratios are equal (all equal 5/2), this is a proportional relationship with constant of proportionality k = 5/2 = 2.5. The equation is y = 2.5x. A proportional relationship always passes through the origin (0,0) when graphed. If you plot these points, they form a straight line through the origin. Be careful about option D: in a proportional relationship, the differences may not be equal to each other (here, y increases by 5 each time and x increases by 2 each time — different amounts). What matters is that the RATIO is constant, not the difference. A constant ratio (y/x = k) defines proportionality.

Question 6: A shirt originally costs $45. It is on sale for 20% off. What is the sale price?

$25
$34
$36 (Correct answer)
$40

Correct answer: $36

20% of $45 = 0.20 × $45 = $9 discount. Sale price = $45 − $9 = $36.

A percent discount problem requires two steps: (1) find the discount amount, (2) subtract from the original price. Discount: 20% of $45 = 0.20 × $45 = $9 Sale price: $45 − $9 = $36 Alternative method: If the discount is 20%, you pay 100% − 20% = 80% of the original price. 80% of $45 = 0.80 × $45 = $36 This single-step method is efficient: multiply the original price by (1 − discount percent). Estimate to check: 20% off means you pay 80%. 80% of $45: 80% of $40 = $32, 80% of $5 = $4. Total = $36. ✓ Percent discount problems are essential life skills for shopping. Understanding that 20% off means you pay 80% is a powerful shortcut. Similarly, a 30% increase means you pay 130% of the original: new price = original × 1.30.

SBAC Math Grade 7 Ratios and Proportions 2

A store sells 3 apples for $1.50.
At this rate, how much do 7 apples cost?