Question

Kieran has $45.00 to purchase supplies to paint the top of a square wooden platform for the school play. The paint roller costs $9.75, and the paint is $17.00 per can. If one can of paint covers approximately 375 square feet, what is the maximum possible length, in feet, of

one side of the wooden platform to the nearest tenth of a foot?
F. 27.3
G. 27.4
H. 27.5
J. 28.0
K. 28.1

Answer 1

Option G. 27.4 ft

Explanation:

step 1

Calculate the maximum number of cans of paint Kieran can buy with $45

Let

x -----> the number of cans of paint

we know that

The number of cans of paints multiplied by it cost plus the cost of a rooler paint must be less than or equal to $45

so

`9.75+17.00x \leq 45`

Solve the inequality for x

Subtract 9.75 both sides

`17.00x \leq 45-9.75`

`17.00x \leq 35.25`

Divide by 17 both sides

`x \leq 2.07\ cans`

so

The maximum number of cans that Kieran can purchase is 2 cans

step 2

Find the maximum area covered with 2 cans of paint

we know that

One can of paint covers approximately 375 square feet

therefore

To find out the area covered with 2 cans multiply 375 by 2

`375(2)=750\ ft^2`

step 3

Find the maximum possible length side of the wooden platform

we know that

The wooden platform is in the shape of a square

so

The area of a square is

`A=b^(2)`

where

b is the length side of the square

we have

`A=750\ ft^2`

substitute and solve for b

`750=b^(2)`

square root both sides

`b=27.4\ ft`