Chapter 1.2, Problem 40HP

(a)

To determine

To write: an expression describing the relationship between the number of quarts and the cups.

Answer to Problem 40HP

The relationship is

“Number of quarts in any number of cups is equal to the one-fourth of the number of cups"

Explanation of Solution

Given:

Number of Cups (c)	4	8	12	16
Number of Quarts (q)	1	2	3	4

Calculation:

First find the relation between them

For, number of cups = 4

Number of quarts $=1=\frac{4}{4}$

For, number of cups = 8

Number of quarts $=2=\frac{8}{4}$

For, number of cups = 12

Number of quarts $=3=\frac{12}{4}$

For, number of cups = 16

Number of quarts $=4=\frac{16}{4}$

Conclusion:

Hence, the relationship is

“Number of quarts in any number of cups is equal to the one-fourth of the number of cups"

(b)

To determine

To write:algebraic expression for number of quarts in c cups.

Answer to Problem 40HP

The number of quarts in c cups is $\frac{c}{4}$

Explanation of Solution

The relationship between number of quarts and number of cups is that

"Number of quarts in any number of cups is equal to the one-fourth of the number of cups"

Now, given that number of cups is "c"

  $\boxed{\frac{c}{4}}$

Since, one- fourth of c is $\frac{c}{4}$ .

Conclusion:

Therefore, number of quarts in c cups is $\frac{c}{4}$

(c)

To determine

To use:the expression in part b to find the number of quarts in 100 cups.

Answer to Problem 40HP

There are 25 quarts in 100 cups.

Explanation of Solution

To find number of quarts in 100 cups, we substitute $c=100$ in the above expression.

  $\frac{c}{4}=\frac{100}{4}=25$

Thus there are 25 quarts in 100 cups.

Conclusion:

Thus there are 25 quarts in 100 cups.