Chapter 1.3, Problem 41IP

(a)

To determine

Write an expression in words that describes the relationship between the number of quarts and the number of cups.

Answer to Problem 41IP

1 Quarts = 4 cups.

Explanation of Solution

Given:

Jacinda used the table below to help convert measurements while she was cooking.

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

Write an expression in words that describes the relationship between the number of quarts and the number of cups.

Concept Used:

1 Quarts = 4 cups.

Thus, 1 Quarts = 4 cups.

(b)

To determine

Write an Algebraic expression that represents the number of quarts in C Cups.

Answer to Problem 41IP

  $\text{c}\text{cups}\text{=}\frac{\text{c}}{4}\text{quartz}$

Explanation of Solution

Given:

Jacinda used the table below to help convert measurements while she was cooking.

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

Write an Algebraic expression that represents the number of quarts in C Cups.

Concept Used:

  $\text{4}\text{cups}\text{=}\text{1}\text{quartz}$

Calculation:

  $\begin{array}{l}\text{4}\text{cups}\text{=}\text{1}\text{quartz}\\ \text{1}\text{cup}\text{=}\frac{\text{1}}{4}\text{quartz}\\ \text{c}\text{cups}\text{=}\frac{\text{c}}{4}\text{quartz}\end{array}$

  $\text{c}\text{cups}\text{=}\frac{\text{c}}{4}\text{quartz}$

Thus, $\text{c}\text{cups}\text{=}\frac{\text{c}}{4}\text{quartz}$

(c)

To determine

Use the expression in Part b to find the number of quarts in 100 cups.

Answer to Problem 41IP

  $100\text{cups}=25\text{quartz}$

Explanation of Solution

Given:

Jacinda used the table below to help convert measurements while she was cooking.

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

Use the expression in Part b to find the number of quarts in 100 cups.

Concept Used:

  $\text{c}\text{cups}\text{=}\frac{\text{c}}{4}\text{quartz}$

Calculation:

  $\begin{array}{l}\text{c}\text{cups}\text{=}\frac{\text{c}}{4}\text{quartz}\\ 100\text{cups}=\frac{100}{4}\text{quartz}=25\text{quartz}\\ 100\text{cups}=25\text{quartz}\end{array}$

  $100\text{cups}=25\text{quartz}$

Thus, $100\text{cups}=25\text{quartz}$