Unit Rates
Find the unit rate: 3 pounds of apples cost $6. What is the cost per pound?
Sales tax is 6%. If an item costs $20, how much tax is added?
$1.20
Determine if the relationship is proportional: (1, 3), (2, 6), (3, 9). Explain why.
yes, each y is 3 times x
Find the slope of the line passing through the points (1, 2) and (3, 6).
2
A coffee shop sells 4 small muffins for $6. If you buy 10 muffins at the same rate, how much will you pay?
$15
A car travels 210 miles on 7 gallons of gas. What is the miles per gallon (unit rate)?
30 miles per gallon
A shirt is marked up by 25% from wholesale price $12. What is the retail price?
$15
Find the constant of proportionality k for the table: x: 2, 4, 6 ; y: 10, 20, 30. Write y = kx
y = 5x
Graphing from slope and point: A line has the slope 2 that passes through (0, 1). What is the equation of the line?
Equation: y = 2x + 1.
A phone plan charges $18 per month for 2 GB of data. How much would a 5‑month subscription cost? How much is 1 GB a month?
Total cost for 5 months 18×5=$90.
Cost per GB per month 18÷2=$9 per GB per month
A recipe uses 4 cups of flour for 6 muffins. What is the flour per muffin as a unit rate (cups per muffin)? Give your answer as a fraction and a decimal.
2/3 and 0.666 or 0.67
Simple interest: If you invest $400 at 4% simple interest per year, how much interest is earned in 3 years? What is the total amount?
$48; $448 in total
A bike rental charges $5 per hour. Write an equation relating cost (C) to hours (h).
C = 5h
Given a graph where the line passes through (−2, 4) and (2, −2), find the slope. Show rise over run and simplify.
-3/2
A store offers a 15% discount on a pair of shoes originally priced at $80, and there is a 6% sales tax applied after the discount. What is the final price after discount and tax?
Discount amount = 0.15×80=$120.15×80=$12. Price after discount = 80−12=$6880−12=$68. Tax = 0.06×68=$4.080.06×68=$4.08. Final price = 68+4.08=$72.0868+4.08=$72.08
A worker earns $360 for 24 hours of work. What is the hourly wage (unit rate)? If the worker works 10 hours, how much will they earn?
$15 per hour; $150
A gratuity of 18% is added to a $48 restaurant bill. What is the tip amount and the total bill?
Tip is $8.64; Total bill $56.64
Given the equation y=2.5x, explain what the number 2.5 represents in terms of unit rate and constant of proportionality. Provide a short real-world example that fits this equation.
2.5 is the constant of proportionality or unit rate (y per x) or slope. Example: If x = number of cookies and y = cost in dollars, cost is $2.50 per cookie.
A line passes through the point (2, −3) and has a slope of −2/3.
Slope-intercept: y = -2/3 - 5/3
A recipe for 8 servings uses 350 grams of sugar. You want to make 20 servings. Using proportional reasoning, how many grams of sugar do you need?
Unit rate sugar per serving = 350÷8=43.75350÷8=43.75 grams per serving. For 20 servings: 43.75×20=87543.75×20=875 grams of sugar.
A map uses a scale where 2.5 cm on the map represents 50 km in real life. What is the unit rate in km per cm? Express as a simplified fraction and a decimal.
20; 20 km/cm
Conversion challenge: A recipe calls for 1500 milliliters of water. Convert this to liters and to gallons (use 1 liter = 1000 mL and 1 gallon ≈ 3.785 liters).
1.5 liters; 0.396 gallons
A relationship is represented by the table: x: 0.5, 1.5, 2.5 ; y: 4, 12, 20. Is this proportional? If yes, find k and write the equation. If no, explain why.
Check ratios: 4 ÷ 0.5 = 8; 12 ÷ 1.5 = 8; 20 ÷ 2.5 = 8. Yes proportional. k = 8. Equation: y = 8x
A graph shows a line through (1, 5) and (4, 2). Find the slope.
-1
A landscaper charges $45 per hour plus a one‑time $30 equipment fee to mow lawns. If a customer pays $255 total, how many hours of work did the landscaper perform? Show equation and solution.
Total cost: 45h+30=255. Subtract fee: 45h=225 Solve: 225÷45=5 hours