A closet in Josh's house is 1 yard by 1 yard. How much would it cost to put a new floor in the closet if the flooring costs $9.00 per square yard?
$
The area of a 1 yard by 1 yard closet is 1 square yard. So, it would cost $9.00 to put a new floor in the closet.
A 3-gallon bucket of paint costs $82.08. What is the price per cup?
$
There are 16 cups in a gallon, so there are 48 cups in a 3-gallon bucket.
To find the price per cup, we can divide the total cost ($82.08) by the number of cups in the bucket (48):
$82.08 ÷ 48 = $1.71
So, the price per cup of paint is $1.71.
Read the following description of a relationship:
A flower shop offers a coupon for $1 off a bouquet of flowers.
Let p represent the price of a bouquet and c represent the cost of the bouquet with the coupon.
This relationship can also be shown in a table. Complete the equation that represents the relationship between p and c.
p c
4 3
5 4
6 5
7 6
c=p–
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Skill IconWrite a two-variable equation from a table (85)Lesson IconLesson: Writing algebraic expressions
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The table shows that when you apply the $1 coupon to a bouquet of flowers, the cost (c) is $1 less than the original price (p). Therefore, the equation that represents the relationship between p and c is:
c = p - 1
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Read the following description of a relationship:
A pizzeria puts 3 basil leaves on each caprese pizza.
Let p represent the number of caprese pizzas and b represent the total number of basil leaves used.
This relationship can also be shown in a table. Complete the equation that represents the relationship between p and b.
p b
5 15
6 18
7 21
8 24
b=
p
The table shows that the number of caprese pizzas (p) is directly proportional to the total number of basil leaves used (b). We can use the information in the table to find the constant of proportionality, which is the number of basil leaves per pizza.
To do this, we can choose any row from the table and divide the total number of basil leaves (b) by the number of pizzas (p). For example, if we choose the first row:
b/p = 15/5 = 3
This tells us that there are 3 basil leaves on each caprese pizza.
Therefore, the equation that represents the relationship between p and b is:
b = 3p
Read the following description of a relationship:
Skaters pay $8 for admission to the Park Creek Ice Rink. They can also rent skates for one dollar per hour.
Let h represent the number of hours of skate rental and t represent the total cost for ice skating.
This relationship can also be shown in a table. Complete the equation that represents the relationship between h and t.
h t
6 14
7 15
8 16
9 17
t=
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answered
4
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35
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The table shows that the total cost (t) for ice skating is not just dependent on the number of hours rented (h), but also includes a fixed cost of $8 for admission to the rink. Therefore, we can write an equation in the form:
t = m × h + b
where m represents the cost per hour of rental and b represents the fixed cost of admission.
To find m, we can look at the change in cost (Δt) for a one-hour increase in rental time (Δh). For example, if we look at the first two rows:
Δt = t2 - t1 = 15 - 14 = 1
Δh = h2 - h1 = 7 - 6 = 1
This tells us that the cost per hour of rental is $1.
To find b, we can choose any row from the table and substitute the values into the equation. For example, if we use the first row:
t = m × h + b
14 = 1 × 6 + b
b = 8
Therefore, the equation that represents the relationship between h and t is:
t = h + 8
o-variable equation
2RE
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Read the following description of a relationship:
Meg is running a lemonade stand. She earns $2 from each cup of lemonade she sells.
Let c represent the number of cups sold and d represent the total earnings in dollars.
This relationship can also be shown in a table. Complete the equation that represents the relationship between c and d.
c d
7 14
8 16
9 18
10 20
d=