6-4 Proportional and Nonproportional Relationships
Determine whether the set of numbers in each table is proportional. Explain.
Write the rate of blue paint to yellow paint for each quart in simplest form.
The rates are not equal. So, the amount of yellow paint is not proportional to the amount of blue paint.
No; the rates are not equal.
Write the rate of ice tea mix to sugar for each quart in simplest form.
Each rate is equal to
. So, the amount of sugar is proportional to the amount of ice tea mix.
Yes; each rate is equal to
.
GASOLINE The cost of 13 gallons of gasoline is $41.47. Write an equation relating cost to the number of gallons of
gasoline. How much does 18.5 gallons of gasoline cost?
Find the constant of proportionality.
or 3.19
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cost is- $3.19
times
the number
of gallons of gas, g. The equation is c = 3.19g.
To find the cost of 18.5 gallons of gas, substitute 18.5 for g.
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6-4 Yes;
Proportional
andtoNonproportional
Relationships
each rate is equal
.
GASOLINE The cost of 13 gallons of gasoline is $41.47. Write an equation relating cost to the number of gallons of
gasoline. How much does 18.5 gallons of gasoline cost?
Find the constant of proportionality.
or 3.19
The cost is $3.19 times the number of gallons of gas, g. The equation is c = 3.19g.
To find the cost of 18.5 gallons of gas, substitute 18.5 for g.
18.5 gallons of gas cost $59.02.
c = 3.19g; $59.02
Determine whether the set of numbers in each table is proportional. Explain.
Write the rates of cans of concentrate to cans of water in simplest form
Each rate is equal to . So, the amount of cans of water is proportional to the amount of cans of concentrate.
Yes; each rate is equal to
.
Write the rates of shaded squares to total squares in simplest form.
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each rate is equal
.
6-4 Yes;
Proportional
andtoNonproportional
Relationships
Write the rates of shaded squares to total squares in simplest form.
The rates are not equal. So, the number of total squares is not proportional to the number of shaded squares.
No; the rates are not equal.
Write the rates of junk e-mails to total e-mails in simplest form.
Each rate is equal to . So, the number of total e-mails is proportional to the number of junk e-mails.
Yes; each rate is equal to
Write the rates of weeks to days in simplest form.
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6-4 Yes;
Proportional
andtoNonproportional Relationships
each rate is equal
Write the rates of weeks to days in simplest form.
Each rate is equal to . So, the number of days is proportional to the number of weeks.
Yes; each rate is equal to .
Write the rates of the heat index to air temperature.
The rates are not equal. So, the air temperature is not proportional to the heat index.
No; the rates are not equal.
Write the rates of jars to jelly beans in simplest form.
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The rates are not equal. So, the air temperature is not proportional to the heat index.
6-4 Proportional and Nonproportional Relationships
No; the rates are not equal.
Write the rates of jars to jelly beans in simplest form.
The rates are not equal. So, the number of jelly beans is not proportional to the number of jars.
No; the rates are not equal.
For Exercises 10 and 11, write and solve an equation.
FINANCIAL LITERACY A store is having a sale where all jeans are
off the regular price. Write an equation
relating the sale price to the regular price. How much would a pair of $29 jeans cost on sale?
Let r = the regular price of jeans
All jeans are
off the regular price. So, the sale price is
Let s = sales price. Then, s = 0.75r.
To find the sale price of a pair of $29 jeans, substitute 29 for r.
s = 0.75r
s = 0.75(29)
s = 21.75
A pair of $29 jeans would cost $21.75 on sale.
s = 0.75r ; $21.75
LAWN SERVICE Luke earned $54 after mowing 3 lawns. Write an equation comparing earnings to lawns
mowed. How much would Luke earn after mowing 7 lawns?
Find the constant of proportionality.
or 18
Luke earns $18 for each lawn mowed.
Let l = the number of lawns mowed, and p = the earnings. Then, p = 18l.
To find out how much Luke would earn after mowing 7 lawns, substitute 7 for l.
p = 18l
p = 18(7)
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p = 126
Luke would earn $126 after mowing 7 lawns.
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A pair of $29 jeans would cost $21.75 on sale.
6-4 sProportional
= 0.75r ; $21.75 and Nonproportional Relationships
LAWN SERVICE Luke earned $54 after mowing 3 lawns. Write an equation comparing earnings to lawns
mowed. How much would Luke earn after mowing 7 lawns?
Find the constant of proportionality.
or 18
Luke earns $18 for each lawn mowed.
Let l = the number of lawns mowed, and p = the earnings. Then, p = 18l.
To find out how much Luke would earn after mowing 7 lawns, substitute 7 for l.
p = 18l
p = 18(7)
p = 126
Luke would earn $126 after mowing 7 lawns.
p = 18l; $126
Copy and complete each table. Determine whether the pattern forms a proportion.
PIZZA Ms. Rollins had an end-of-year pizza party for the chess team. At the party, every 2 students had 5 slices of
pizza.
Number of Students
s
Slices of Pizza
2
4
6
8
10
Write the rates of number of students to slices of pizza in simplest form.
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p = 126
Luke would earn $126 after mowing 7 lawns.
6-4 Proportional and Nonproportional Relationships
p = 18l; $126
Copy and complete each table. Determine whether the pattern forms a proportion.
PIZZA Ms. Rollins had an end-of-year pizza party for the chess team. At the party, every 2 students had 5 slices of
pizza.
Number of Students
s
Slices of Pizza
2
4
6
8
10
Write the rates of number of students to slices of pizza in simplest form.
Each rate is equal to . So, the number of slices of pizza is proportional to the number of students.
yes
AMUSEMENT PARKS Admission to an amusement park is $4 plus $1.50 per ride.
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6-4 Proportional and Nonproportional Relationships
AMUSEMENT PARKS Admission to an amusement park is $4 plus $1.50 per ride.
Number of Rides
r
1
2
3
4
5
Cost
1.5r + 4
1.5(1) + 4 = $5.50
1.5(2) + 4 = $7.00
1.5(3) + 4 = $8.50
1.5(4) + 4 = $10.00
1.5(5) + 4 = $11.50
Write the rates of number of rides to cost in simplest form.
The rates are not equal. So, the cost is not proportional to the number of rides.
no
PARTY PLANNING It will cost $7 per person to hold a birthday party at the recreation center.
Number of Guests
g
6
7
8
9
10
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Cost
7g
7(6) = $42
7(7) = $49
7(8) = $56
7(9) = $63
7(10) = $70
Write the rates of number of guests to cost in simplest form.
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6-4 Proportional and Nonproportional Relationships
PARTY PLANNING It will cost $7 per person to hold a birthday party at the recreation center.
Number of Guests
g
6
7
8
9
10
Cost
7g
7(6) = $42
7(7) = $49
7(8) = $56
7(9) = $63
7(10) = $70
Write the rates of number of guests to cost in simplest form.
Each rate is equal to
. So, the cost is proportional to the number of guests.
yes
Complete each conversion. Round to the nearest hundredth, if necessary.
cm
10.16
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gal
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6-4 Proportional and Nonproportional Relationships
Complete each conversion. Round to the nearest hundredth, if necessary.
cm
10.16
gal
1.32
kg
681
_m
12.8
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140 miles on 6 gallons
rate. Round to the nearest tenth, if necessary.
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6-4 Proportional and Nonproportional Relationships
12.8
Express each rate as a unit rate. Round to the nearest tenth, if necessary.
140 miles on 6 gallons
The unit rate is 23.3 miles per gallon.
23.3 miles per gallon
19 yards in 2.5 minutes
The unit rate is 7.6 yards in 1 minute.
7.6 yards per minute
236.7 miles in 4.5 days
The unit rate is 52.6 miles per day.
52.6 miles per day
331.5 pages in 8.5 weeks
The unit rate is 39 pages per week.
39 pages per week
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