← Back to the Proportional Equations worksheet
Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: 7.RP.A.2c · Level: Grade 7
Problem 1 Car Wash Equation
The price per car is the constant, so c = 7.5n.
For n = 12: 7.5 × 12 = 90.
Answer: c = 7.5n; $90
Problem 2 Pay Table Equation
25 ÷ 2 = 12.5, 62.5 ÷ 5 = 12.5, 100 ÷ 8 = 12.5.
Answer: p = 12.5h
Problem 3 Flour and Batches
34 ÷ 12 = 32, 3 ÷ 2 = 32, 92 ÷ 3 = 32.
Answer: f = 1.5b
Problem 4 Equation from a Graph
Use (8, 20): 20 ÷ 8 = 2.5. Check (3, 7.5): 7.5 ÷ 3 = 2.5.
Answer: y = 2.5x
Problem 5 Taxi Fare per Mile
C = 2.2d.
2.2 × 7.5 = 16.5.
Answer: C = 2.2d; $16.50
Problem 6 Missing Values from an Equation
y = 6.4 × 5 = 32.
x = 51.2 ÷ 6.4 = 8.
Answer: y = 32; x = 8
Problem 7 Total Cost with t = pn
t = 1.35n.
18 pens: 1.35 × 18 = 24.30.
$40.50: 40.50 ÷ 1.35 = 30.
Answer: $24.30; 30 pens
Problem 8 Gas Used and Miles Driven
2.5 ÷ 60 = 124, 6.25 ÷ 150 = 124, 8.75 ÷ 210 = 124.
g = m24.
372 ÷ 24 = 15.5 gallons.
11 × 24 = 264 miles.
Answer: g = m ÷ 24; 15.5 gallons; 264 miles
Problem 9 Slow Growth Graph
4 ÷ 10 = 0.4 and 8 ÷ 20 = 0.4.
y = 0.4x.
0.4 × 35 = 14.
Answer: y = 0.4x; y = 14
Problem 10 Snail Equation
k = 3 ÷ 8 = 38, so d = 38t.
20 minutes: 38 × 20 = 7.5 feet.
12 feet: 12 ÷ 38 = 12 × 83 = 32 minutes.
Answer: d = 38t; 7.5 feet; 32 minutes
Problem 11 Bead Ratio Equation
r = 74b.
20 blue: 74 × 20 = 35 red.
56 red: 56 ÷ 74 = 56 × 47 = 32 blue.
Answer: r = 74b; 35 red beads; 32 blue beads
Problem 12 Which Equations Are Proportional
A proportional equation has the form y = kx.
(a) k = 7. (b) Adds 7, so not proportional. (c) Division by x, not proportional. (d) k = 0.7.
Answer: (a) and (d) are proportional
Problem 13 One Point Gives the Equation
k = 20 ÷ 16 = 1.25.
y = 1.25x.
1.25 × 44 = 55.
Answer: y = 1.25x; y = 55
Problem 14 Interpreting an Equation
55 is the unit rate: 55 miles per hour.
(1, 55): in 1 hour the bus travels 55 miles.
(3, 165): 55 × 3 = 165, so in 3 hours the bus travels 165 miles.
Answer: 55 miles per hour; (1, 55) is the unit rate; (3, 165) is the distance after 3 hours
Problem 15 Biking Speed Comparison
Marco: 21 ÷ 2 = 10.5, 31.5 ÷ 3 = 10.5, 52.5 ÷ 5 = 10.5, so d = 10.5t.
Jenna: 11.5 > 10.5, so she is faster.
After 4 hours: Jenna 46 miles, Marco 42 miles. 46 − 42 = 4.
Answer: Jenna is faster; she is 4 miles ahead after 4 hours
Problem 16 Savings Graph Versus Equation
Sam: 32.5 ÷ 5 = 6.5, so y = 6.5x.
Tia saves 7 per week, which is 0.50 more than Sam.
After 12 weeks: Sam 6.5 × 12 = 78, Tia 7 × 12 = 84, and 84 − 78 = 6.
Answer: Tia saves more per week; she has $6 more after 12 weeks
Problem 17 Two Printers
P: 24 ÷ 2 = 12, so p = 12m. Q: 39 ÷ 3 = 13, so p = 13m.
P needs 156 ÷ 12 = 13 minutes. Q needs 156 ÷ 13 = 12 minutes.
Answer: p = 12m and p = 13m; Q finishes 1 minute sooner
Problem 18 Trip Fuel Cost
Hybrid: 270 ÷ 45 = 6 gallons, cost 6 × 3.60 = $21.60.
Truck: 6 ÷ 90 = 115 and 9 ÷ 135 = 115, so g = m ÷ 15. For 270 miles, 270 ÷ 15 = 18 gallons, cost 18 × 3.60 = $64.80.
64.80 − 21.60 = 43.20.
Answer: The truck costs $43.20 more
Problem 19 Sales Tax Equation
t = 0.0825p.
$64: tax = 0.0825 × 64 = 5.28, total = 64 + 5.28 = 69.28.
Tax $9.90: p = 9.90 ÷ 0.0825 = 120.
Answer: t = 0.0825p; tax $5.28, total $69.28; price $120
Problem 20 Equation from Two Points
14 ÷ 8 = 1.75 and 35 ÷ 20 = 1.75, so k = 1.75 = 74.
y = 1.75x.
52 × 1.75 = 91.
105 ÷ 1.75 = 60.
Answer: y = 1.75x; y = 91; x = 60