Unit Rates
A store sells 15 pencils for $9. What is the cost of 1 pencil?
$0.60
A recipe uses 5 cups of juice to make 15 servings.
How many servings can be made with 8 cups of juice?
24 servings
15% of 40
6
9x − 2x
7x
Student says
9x − 4x = 13x
What's wrong?
Should be 5x
A cyclist rides 84 miles in 4 hours.
What is the unit rate?
21 miles per hour
The equation is
y = 6x
Find y when x = 9.
54
A bike costs $120.
It is 30% off.
Sale price?
$84
7m + 9 − 5m + 3
2m + 12
Student says
30% of 200 = 230
What's wrong?
30% of 200 = 60.
A printer prints 540 pages in 9 minutes.
How many pages per minute?
60 pages
A movie theater charges $14 per ticket.
Write the equation.
y=14x
A meal costs $55.
Add 8% tax.
$59.40
14y − 8 + 5y − 6
19y - 14
Student says
8 + 2y = 10y
What's wrong?
Can't combine constants and variable
A grocery store sells 8 oranges for $6.40.
How much does 1 orange cost?
$0.80
A grocery store sells 8 pounds of apples for $20.
If the relationship is proportional, how much will 14 pounds cost?
$35
A sweatshirt costs $72.
Increase the price 25%.
$90
20a + 7 − 12a − 5
8a + 2
Student says
$80 with 25% off costs $65.
Correct?
No. It costs $60.
A faucet fills 90 gallons in 6 minutes.
How many gallons in 15 minutes?
225 gallons
A graph represents a proportional relationship and passes through the points (3, 18) and (7, 42).
What is the constant of proportionality?
A. 5
B. 6
C. 7
D. 9
B. 6
A phone costs $250.
It increases 20%, then is discounted 10%.
Final price?
$270
Simplify
18x + 12 − 7x − 15
11x - 3
Student says
The graph is proportional because it's a straight line.
What's missing?
It must also pass through (0,0).