Unit Rates
A store sells notebooks at a constant price: 2 cost $5.50, 5 cost $13.75, and 8 cost $22. What is the cost per notebook?
$2.75 per notebook. Divide 5.50 by 2.
Six identical admission tickets cost $51. Let x be the number of tickets and y be the total cost in dollars. Write an equation relating x and y.
y = 8.50x, because 51 ÷ 6 = 8.50 dollars per ticket.
A school club had 40 members last year and has 50 this year. What is the percent increase?
25% increase. (50 − 40) ÷ 40 × 100 = 25%.
A $60 sweatshirt is discounted 15%. What is the sale price before tax?
$51. Discount: 60 × 0.15 = $9; 60 − 9 = 51.
A meal costs $46 before tax. A customer tips 15% of that amount. How much is the tip?
$6.90. 46 × 0.15 = 6.90.
A recipe makes 30 muffins using 1⅔ cups of flour. How many muffins can be made per cup of flour?
18 muffins per cup. 30 ÷ (5/3) = 18.
A proportional graph has hours worked on the horizontal axis and earnings in dollars on the vertical axis. It passes through (0, 0), (2, 28), and (5, 70). Write its equation.
y = 14x. The unit rate is $14 per hour.
A bus route took 60 minutes before a change and now takes 45 minutes. What is the percent decrease?
25% decrease. (60 − 45) ÷ 60 × 100 = 25%.
Two stores sell the same $80 shoes. Store A offers 30% off; Store B offers 20% off. How much less do the shoes cost at Store A?
$8 less. Store A: $56; Store B: $64; 64 − 56 = 8.
A game costs $56 before 7.5% sales tax. Find the sales tax and the total cost.
$4.20 tax; $60.20 total. 56 × 0.075 = 4.20.
A runner travels 5⅗ miles in ⅘ hour. What is the average speed in miles per hour?
7 miles per hour. (28/5) ÷ (4/5) = 7.
A recipe table pairs cups of oats x with granola bars y: (¾, 9), (1½, 18), and (2¼, 27). Find the constant of proportionality and write an equation.
12 bars per cup; y = 12x. Divide 9 by ¾.
A shop buys a lamp for $36 and marks up its cost by 45%. What is the selling price before tax?
$52.20. Markup: 36 × 0.45 = $16.20; 36 + 16.20 = 52.20.
A camera costs $250. It is discounted 20%, then an extra 15% is taken off the sale price. What is the final price before tax?
$170. 250 × 0.80 = $200; 200 × 0.85 = $170.
A meal costs $64 before tax and tip. Sales tax is 8%; the tip is 18% of the pretax bill. Find the total cost.
$80.64. Tax: $5.12; tip: $11.52; 64 + 5.12 + 11.52 = 80.64.
Nina earns $31.50 for 2¼ hours of dog walking. At the same rate, how much will she earn for 3¾ hours?
$52.50. Hourly rate: 31.50 ÷ 2.25 = $14; 14 × 3.75 = 52.50.
A proportional graph shows gallons of water y after x minutes. The point (4, 30) is on the graph. What does the point (1, 7.5) mean? How many gallons flow in 14 minutes?
7.5 gallons flow in 1 minute. In 14 minutes, 7.5 × 14 = 105 gallons.
A store buys a chair for $72 and marks up its cost by 35%. Find the selling price to the nearest dollar.
$97. The unrounded price is 72 × 1.35 = $97.20.
A $160 bicycle is discounted 25%, then 6% sales tax is applied to the sale price. What is the total cost?
$127.20. Sale price: 160 × 0.75 = $120; tax: 120 × 0.06 = $7.20.
Friends have a $42.50 lunch bill before tax and tip. Sales tax is 8%. They tip 20% of the amount AFTER tax. Find the sales tax and the final total.
$3.40 tax; $55.08 total. After tax: $45.90; tip: 45.90 × 0.20 = $9.18.
A machine fills 7½ liters in ⅚ minute. At this rate, how many liters does it fill in 2⅓ minutes?
21 liters. 7.5 ÷ (5/6) = 9 liters per minute; 9 × (7/3) = 21.
A club orders 8 identical shirts for $62. A student writes x = 7.75y, where x is shirts and y is cost in dollars. Correct the equation, then find the cost of 14 shirts.
y = 7.75x. Each shirt costs 62 ÷ 8 = $7.75. Fourteen shirts cost $108.50.
An admission price rises from $24 to $30. A student says the increase is 20% because 6 ÷ 30 = 0.20. Explain the mistake and find the correct percent increase.
Divide by the original price, $24. (30 − 24) ÷ 24 = 0.25, so the increase is 25%.
A $200 jacket is discounted 30%, then an additional 20% is taken off the sale price. A student claims this is 50% off overall. Find the final price and the actual overall percent discount.
$112; 44% off overall. 200 × 0.70 × 0.80 = 112. Savings: $88; 88 ÷ 200 × 100 = 44%.
A restaurant bill is $75 before tax and tip. Sales tax is 8%. Ana tips 20% of the pretax bill; Ben tips 20% of the after-tax bill. Find each total and how much more Ben pays.
Ana: $96. Ben: $97.20. Tax is $6; Ana tips $15; Ben tips 20% of $81 = $16.20. Ben pays $1.20 more.