Chapter 6.7, Problem 28SR

a)

To determine

To set up: An equation that is used to find g, the number of gallons of apple cider when b umber of bushels are given.

Answer to Problem 28SR

Required equation relating two given quantities be $g=3b$

Explanation of Solution

Given information: 

A following table that shows different amounts of apple bushels and gallons of apple cider:

  

Concept used: Following formula is used here,

Total gallons of apple cider = gallons per bushel ˟ total number of bushels

It is because given values show that both variables are in proportion as each ratio between variable b and g is same.

Calculation:

By table, each corresponding values between b and g are in proportion, so gallon per bushel be 3 (as given in table also)

So, on plug in concerned variables and above value in said formula,

  $\text{g}=3\text{b}$

That is the equation, inter-relates given variables.

Based on above calculation, total $\text{g}=3\text{b}$ and total bushels required to make 54 gallon of cider be 18.

b)

To determine

To calculate: Total bushels to make 54 gallons of cider.

Answer to Problem 28SR

Total 18 bushels are needed to make 54 gallons of cider.

Explanation of Solution

Given information: 

A following table that shows different amounts of apple bushels and gallons of apple cider:

  

Concept used:

Following formula is used here,

Total gallons of apple cider = gallons per bushel ˟ total number of bushels

It is because given values show that both variables are in proportion as each ratio between variable b and g is same.

Calculation:

It is given 54 gallons of cider or $g=\mathrm{54\; ˟}$

So, on dividing each side by 3,

  $b=\frac{54}{3}=18$

Based on above calculation, total bushels required to make 54 gallon of cider be 18.