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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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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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=
The table shows that Meg earns $2 for each cup of lemonade she sells. Therefore, the total earnings in dollars (d) is directly proportional to the number of cups sold (c). We can use the information in the table to find the constant of proportionality, which is the earnings per cup.
To do this, we can choose any row from the table and divide the total earnings (d) by the number of cups sold (c). For example, if we choose the first row:
d/c = 14/7 = 2
This tells us that Meg earns $2 for each cup of lemonade she sells.
Therefore, the equation that represents the relationship between c and d is:
d = 2c
Read the following description of a relationship:
A charity has been planting trees in community gardens around the city. In each garden, the charity plants 6 fewer plums tree than apple trees.
Let a represent the number of apple trees planted in a garden and p represent the number of plum trees planted in the garden.
This relationship can also be shown in a table. Complete the equation that represents the relationship between a and p.
a p
7 1
8 2
9 3
10 4
p=
The table shows that the number of plum trees planted in a garden (p) is directly related to the number of apple trees planted in a garden (a) by a fixed difference of 6 trees. We can express this relationship as:
p = a - 6
Therefore, the equation that represents the relationship between a and p is:
p = a - 6
Read the following description of a relationship:
Every edition of Deb's favorite sports magazine includes 11 pages of ads, but the rest of the magazine is filled with articles.
Let t represent the total number of pages in the magazine and a represent the number of pages of articles.
This relationship can also be shown in a table. Complete the equation that represents the relationship between t and a.
t a
12 1
13 2
14 3
15 4
a=
The table shows that the number of pages of articles (a) is dependent on the total number of pages in the magazine (t), which includes 11 pages of ads and the remaining pages of articles. Therefore, we can write an equation in the form:
t = a + 11
Solving for a, we get:
a = t - 11
Therefore, the equation that represents the relationship between t and a is:
a = t - 11
Read the following description of a relationship:
Jill is making cheese trays for a party. Each tray has 11 more slices of cheddar than Swiss.
Let s represent the number of slices of Swiss cheese on a tray and c represent the number of slices of cheddar cheese on that tray.
This relationship can also be shown in a table. Complete the equation that represents the relationship between s and c.
s c
3 14
4 15
5 16
6 17
c=
The table shows that the number of slices of cheddar cheese on a tray (c) is directly related to the number of slices of Swiss cheese on the same tray (s) by a fixed difference of 11. We can express this relationship as:
c = s + 11
Therefore, the equation that represents the relationship between s and c is:
c = s + 11
Read the following description of a relationship:
A contest is open to teams of 10 people each.
Let t represent the number of teams entering the contest and p represent the total number of people.
Complete the equation that represents the relationship between t and p.
p=
The relationship between the number of teams entering the contest (t) and the total number of people (p) is given by the product of the number of teams and the number of people per team, which is 10:
p = 10t
Read the following description of a relationship:
There are 7 days in a week.
Let w represent the number of weeks and d represent the corresponding number of days.
Complete the equation that represents the relationship between w and d.
d=
The relationship between the number of weeks (w) and the corresponding number of days (d) is given by the product of the number of weeks and the number of days per week, which is 7:
d = 7w
Read the following description of a relationship:
Every day at his bakery, Greg bakes 6 fewer bagels than muffins.
Let m represent the number of muffins and b represent the number of bagels.
Complete the equation that represents the relationship between m and b.
b=
The relationship between the number of muffins (m) and the corresponding number of bagels (b) is given by a fixed difference of 6 bagels:
b = m - 6
Read the following description of a relationship:
Each location of a chain restaurant employs 14 more waiters than cooks.
Let c represent the number of cooks and w represent the number of waiters.
Complete the equation that represents the relationship between c and w.
w=
The relationship between the number of cooks (c) and the corresponding number of waiters (w) is given by a fixed difference of 14 waiters:
w = c + 14
Read the following description of a relationship:
Ed earns spending money by walking his neighbors' dogs. He earns $13 an hour.
Let h represent the number of hours Ed works and d represent the total earnings in dollars.
Complete the equation that represents the relationship between h and d.
d=
The relationship between the number of hours Ed works (h) and the corresponding total earnings in dollars (d) is given by multiplying the number of hours by the hourly rate, which is $13:
d = 13h