Question

The number of pounds in a bag of flour varies

directly with the number of ounces. Write a direct
variation equation that describes the relationship.
Use your equation to determine the number of
pounds in 152 ounces.
The number of nencils for sale varies directly with th

Answer 1

Part 5)

a)
`y=(1)/(16)x`

b)
`y=9.5\ pounds`

Part 6)

a)
`y=50x`

b)
`y=700\ pencils`

Explanation:

The complete questions in the attached figure

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 5) The number of pounds in a bag of flour varies directly with the number of ounces. Write a direct variation equation that describes the relationship. Use your equation to determine the number of pounds in 152 ounces.

Part a) Write a direct variation equation that describes the relationship

Let

x ------> number of ounces

y ----> number of pounds

Observing the graph we have

The point (16,1)

so

`x=16\ ounces`

`y=1\ pounds`

Fin the value of the constant of proportionality k

`k=y/x`

substitute the values

`k=(1)/(16)(pounds)/(ounce)`

The equation of the direct variation is

`y=(1)/(16)x`

Part b) Use your equation to determine the number of pounds in 152 ounces

we have

`y=(1)/(16)x`

For
`x=152\ ounces`

substitute the value of x in the equation and solve for y

`y=(1)/(16)(152)`

`y=9.5\ pounds`

Part 6) The number of pencils for sale varies directly with the number of boxes. Write a direct variation equation that describes the relationship. Use your equation to determine the number of pencils in 14 boxes.

Part a) Write a direct variation equation that describes the relationship

Let

x ------> number of boxes

y ----> number of pencils

Observing the graph we have

The point (1,50)

so

`x=1\ box`

`y=50\ pencils`

Fin the value of the constant of proportionality k

`k=y/x`

substitute the values

`k=(50)/(1)=50(pencils)/(box)`

The equation of the direct variation is

`y=50x`

Part b) Use your equation to determine the number of pencils in 14 boxes.

we have

`y=50x`

For
`x=14\ boxes`

substitute the value of x in the equation and solve for y

`y=50(14)`

`y=700\ pencils`