Question

A 3-pound bag of apples costs $5.25. What is the unit price of a pound of apples?

a) $1.25 b) $1.75 c) $2.25 d) $2.75 per pound
At this rate, how many pounds of apples can be purchased for $17.50?
a) 8 b) 9 c) 10 d) 11 pounds of apples
Let x represent the number of pounds of apples and y the total cost of the apples. What is the equation that represents the direct variation between the total cost of the apples and the number of pounds of apples?
a) y = 1.25x
b) y = 1.75x
c) y = 2.25x
d) y = 2.75x

Answer 1

1) $5.25/3 lb = $1.75/lb or b

2) 1.75x=17.50
x= 10 lbs, or c

3) b

Answer 2

Part a) A 3-pound bag of apples costs $5.25. What is the unit price of a pound of apples?

we know that

To find the unit price divide the total cost by the total pounds

so

`(5.25)/(3) =1.75(\$)/(pound)`

therefore

the answer Part a) is the option b

`\$1.75`

Part b) At this rate, how many pounds of apples can be purchased for $17.50?

by proportion

`(1)/(1.75) (pound)/(\$) =(x)/(17.5) (pound)/(\$) \\ \\1.75*x=17.5\\ \\x=17.5/1.75 \\ \\x=10\ pounds`

therefore

the answer Part b) is the option c

`10\ pounds`

Part c) Let x represent the number of pounds of apples and y the total cost of the apples. What is the equation that represents the direct variation between the total cost of the apples and the number of pounds of apples?

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form
`y/x=k` or
`y=kx`

In this problem the constant of proportionality k is equal to the unit price of a pound of apples

so

`k=1.75(\$)/(pound)`

The linear equation is equal to

`y=1.75x`

therefore

the answer Part c) is the option b

`y=1.75x`