Answer:
Part 1)
a) The unit rate is $2.5 per pumpkin
b) The units rate is $4.5 per pound
c) The unit rate is 1 mile/hour
d) The unit rate is 2.67 mph
Part 2)
a) x=20
b) x=13
c) x=30
d) x=3
e) x=10
f) x=56
g) x=2.5
h) x=6
Step-by-step explanation:
Part 1)
we know that
A unit rate is a ratio that has a denominator of 1
Part a) we know that
Andy buys 400 pumpkins for $1,000
To find out the unit rate divide the total cost by the number of pumpkin
so
1,000/400=$2.5/1 -----> the denominator is equal to 1
Part b) Sonia spend $13.50 on 3 lbs of candy What is the price of one pound?
To find the price of one lb of candy, find out the unit rate, so divide the total cost by the number of pounds
$13.50/3=$4.5 per pound
Part c) Sam walks 4 miles in 4 hours What is Sam's speed per hour?
To find the unit rate divide the total distance by the total time
so
4/4=1 mile/hour
Part d) Arnold walks 2 miles in 45 min What is his speed in mph?
To find the unit rate divide the total distance by the total time but first convert minutes to hours
45 min=45/60=0.75 h
2/0.75=2.67 mph
Part 2)
we know that
Equivalent fractions are fractions that are equal in value. To determine if two fractions are equivalent, cross-multiply the fractions--multiply the numerator of each fraction by the denominator of the other. The fractions are equivalent if the products are the same
Part a) we have
[tex]\frac{5}{10}=\frac{x}{40}[/tex]
Multiply in cross
[tex]5*40=10*x[/tex]
[tex]200=10x[/tex]
Divide by 10 both sides
[tex]x=20[/tex]
Part b) we have
[tex]\frac{x}{4}=\frac{52}{16}[/tex]
Multiply in cross
[tex]16*x=52*4[/tex]
[tex]16x=208[/tex]
Divide by 16 both sides
[tex]x=13[/tex]
Part c) we have
[tex]\frac{6}{7}=\frac{x}{35}[/tex]
Multiply in cross
[tex]6*35=7*x[/tex]
[tex]210=7x[/tex]
Divide by 7 both sides
[tex]x=30[/tex]
Part d) we have
[tex]\frac{10}{x}=\frac{80}{24}[/tex]
Multiply in cross
[tex]10*24=80*x[/tex]
[tex]240=80x[/tex]
Divide by 80 both sides
[tex]x=3[/tex]
Part e) we have
[tex]\frac{50}{10}=\frac{x}{2}[/tex]
Multiply in cross
[tex]50*2=10*x[/tex]
[tex]100=10x[/tex]
Divide by 10 both sides
[tex]x=10[/tex]
Part f) we have
[tex]\frac{5}{7}=\frac{40}{x}[/tex]
Multiply in cross
[tex]5*x=40*7[/tex]
[tex]5x=280[/tex]
Divide by 5 both sides
[tex]x=56[/tex]
Part g) we have
[tex]\frac{1}{x}=\frac{10}{25}[/tex]
Multiply in cross
[tex]1*25=10*x[/tex]
[tex]25=10x[/tex]
Divide by 10 both sides
[tex]x=2.5[/tex]
Part h) we have
[tex]\frac{5}{x}=\frac{20}{24}[/tex]
Multiply in cross
[tex]5*24=20*x[/tex]
[tex]120=20x[/tex]
Divide by 20 both sides
[tex]x=6[/tex]
