Question

Can you help me answer these three questions plz. also show your work, please

For Exercises 10 –12, assume all situations are proportional.


6. CLASSES For every girl taking classes at the martial arts school, there are 3 boys who are taking classes at the
school. If there are 236 students taking classes, write and solve a proportion to predict the number of boys taking
classes at the school.

7. BICYCLES An assembly line worker at Rob’s Bicycle factory adds a seat to a bicycle at a rate of 2 seats in 11
minutes. Write a proportion relating the number of seats s to the number of minutes m. At this rate, how long will it
take to add 16 seats? 19 seats?

8. PAINTING Lisa is painting a fence that is 26 feet long and 7 feet tall. A gallon of paint will cover 350 square feet.
Write and solve a proportion to determine how many gallons of paint Lisa will need.

Answer 1

Part 6) 177 boys

Part 7) a) 88 minutes b) 104.5 minutes

Part 8) 1 gallon

Explanation:

we know that

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

Part 6)

Let

x ----> the number of girls taking classes at the school

y ----> the number of boys taking classes at the school

we know that

`(x)/(y)=(1)/(3)`

`x=(1)/(3)y` ----> equation A

`x+y=236` ----> equation B

substitute equation A in equation B and solve for y

`(1)/(3)y+y=236`

`(4)/(3)y=236`

`y=236(3)/4`

`y=177\ boys`

Part 7)

Let

s ----> the number of seats

m ---> the number of minutes

we know that

`(s)/(m)=(2)/(11)` ---> equation A

Part a) At this rate, how long will it take to add 16 seats?

For s=16 seats

substitute in the equation A and solve for m

`(16)/(m)=(2)/(11)`

`m=16(11)/2`

`m=88\ min`

Part b) At this rate, how long will it take to add 19 seats?

For s=19 seats

substitute in the equation A and solve for m

`(19)/(m)=(2)/(11)`

`m=19(11)/2`

`m=104.5\ min`

Part 8)

Let

x ----> the number of gallons

y ----> the area is square feet

we know that

`(x)/(y)=(1)/(350)` ----> equation A

step 1

Find the area of the fence

`A=(26)(7)=182\ ft^2`

step 2

Determine how many gallons of paint Lisa will need

For y=182 ft^2

substitute in the equation A and solve for x

`(x)/(182)=(1)/(350)`

`x=(182)/(350)`

`x=0.52\ gal`

Round to the nearest whole number

`x= 1\ gal`