Unit Rate
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Proportions
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Proportions
A store sells 6 notebooks for $8.40. What is the unit price in dollars per notebook?
$1.40 per notebook
8.40÷6=1.40
A $48 backpack is discounted by 25%. What is the amount of the discount?
$12
25% of 48
0.25×48=12
A temperature of -7°C increases by 12°C.
What is the new temperature?
Justify with a calculation.
5°C
-7+12=5
A student solves 6x+8=50. What is the value of x?
x=7
Subtract 8, then divide by 6.
A map uses a scale of 1 inch = 5 miles. A distance on the map is 3 inches. What is the actual distance?
15 miles
3×5=15
A runner travels 2.4 miles in 18 minutes at a constant rate. At this rate, how many miles will the runner travel in 1 hour?
8 miles
2.4÷18= 2/15 mile per minute.
2/15*60=8
A $120 jacket is discounted 25%, then 8% sales tax is added to the sale price. What is the final price?
$97.20
Discounted price: 120×0.75=90
With tax: 90×1.08=97.20
Evaluate: −4(6−11)+3
23
Work:
6−11=−5
−4(−5)+3=20+3=23
Solve: 3(-4a+7)<-15
t>3
A fair six-sided die is rolled twice. What is the probability of rolling an even number both times?
1/4
P(even) = 3/6=1/2
Two rolls: 1/2*1/2=1/4
Store A sells 18 batteries for $13.50. Store B sells 10 batteries for $7.20. Which store has the lower unit price?
Store B
Cost /per/ battery
Store A: 13.50÷18=0.75
Store B: 7.20÷10=0.72
Store B is cheaper per battery.
The price of a bicycle increases from $80 to $92. What is the percent increase?
15%
Increase: 92 − 80 = 12
Percent increase: 12 ÷ 80 = 0.15 = 15%
Evaluate: −24÷6+3(−4) ^2
44
−24÷6=−4-
(−4)2=16
3×16=48
−4+48=44
Company A charges $25 plus $4 per hour. Company B charges $10 plus $6 per hour.
1.Write an expression to represent the cost at each company.
2. Which company is cheaper for 8 hours?
1. Company A: 25+4h
Company B: 10+6h
2. Company A is cheaper after 8 hours.
Company A: 25+4(8)=57
Company B: 10+6(8)=58
A scale drawing uses 2 cm = 3 m. A length on the drawing is 8 cm. What is the actual length?
12 m
8÷2=4 scale groups
4×3=12
A smoothie shop uses 6 cups of fruit to make 9 smoothies. Another shop uses 10 cups of fruit to make 15 smoothies. Which shop uses less fruit per smoothie?
Neither; they use the same amount.
Cups of fruit /per/ smoothie
Shop 1: 6div9=2/3
Shop 2: 10div15=2/3
A store offers 20% off all items. After the discount, 10% sales tax is applied. If the original price is $150, what is the final price?
$132
After discount: 150×0.80=120
After tax: 120×1.10=132
At midnight the air temperature was -3°C. By noon the next day, the temperature increased by 22°C. By that evening the temperature decreased 19°C. What was the evening temperature?
0°C
-3+22=19
19-19=0
A movie theater charges $2 for a service fee plus $9 per ticket. If the total cost is $47, how many tickets were bought? Justify your answer with an equation and its solution.
5 tickets
9x+2=47
9x=45
x=5
Set A: 10, 12, 14, 16, 18
Set B: 5, 10, 15, 20, 25
Which set has the greater interquartile range? What does that mean?
Set B; its middle half is more spread out.
Set A: Q1=12, Q3=16, IQR=4
Set B: Q1=10, Q3=20, IQR=10
A job pays $45 for 3 hours and $105 for 7 hours. A second job pays according to y=14x, where x is hours and y is dollars. Which job pays more per hour, and how much more would someone earn after 8 hours at the higher-paying job?
First job; $8 more
First job: 45÷3=15 dollars per hour
Second job: 14 dollars per hour
Difference: 15−14=1 dollar per hour
For 8 hours: 1×8=8
A laptop originally costs $800. It is reduced by 18%, and then a $50 rebate is applied. What is the percent decrease from the original price to the final price?
24.25%
Discount: 800×0.18=144
Sale price: 800−144=656
Final price: 656−50=606
Decrease: 800−606=194
Percent decrease: 194÷800=0.2425=24.25%
A hiker starts at 250 feet above sea level. She descends 400 feet, climbs 175 feet, and then descends 125 feet. Write an expression and find her final elevation.
−100 feet
250−400+175−125=−100
A gym charges a $30 sign-up fee and $12 per month. Write an equation for the total cost, C, after mmm months. Then find how many months it takes for the total cost to be $150.
C=12m+30; 10 months
150=12m+30
120=12m
m=10
A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. One marble is selected, replaced, and then another marble is selected. What is the probability of selecting a red marble first and a blue marble second?
3/20
Total = 10 marbles
P(red) = 5/20
P(blue) = 3/10
5/10*3/10=15/100=3/20