Writing and Interpreting Expressions

Question

Mixture Table
Number of Pounds Price per Pound Cost
Raisins x 3.50 3.5x
Nuts 4.75
Mixture 20 4.00 80
Question 1
The Bee Healthy store sells a mixture of raisins and nuts. Twenty pounds are in each batch. By looking at the information given on the table, which expression could represent the number of pounds of nuts needed to make the mixture?
Responses
A x + 20x + 20
B x − 20

x − 20
C 20 − x20 − x
D 20 + x20 + x
Question 2
Which expression could represent the total cost of the nuts?
Responses
A 4.75(x − 20)4.75(x − 20)
B 4.75x4.75x
C 4.75(20 − x)4.75(20 − x)
D 4.75(20 + x)

Answer 1

To solve the questions based on the given mixture table:

Question 1

The problem states that the total weight of the mixture is 20 pounds, which is made up of raisins and nuts. You are given the number of pounds of raisins as \( x \). Therefore, the remaining pounds for nuts can be represented as:

\[ \text{Nuts} = 20 - x \]

Thus, the expression that could represent the number of pounds of nuts needed to make the mixture is:

C: \( 20 - x \)

Question 2

To find the expression representing the total cost of the nuts, we know the price per pound of nuts is $4.75. Since the number of pounds of nuts is \( 20 - x \) (from Question 1), the total cost for the nuts can be calculated as:

\[ \text{Total Cost of Nuts} = \text{Price per Pound} \times \text{Pounds of Nuts} = 4.75(20 - x) \]

Therefore, the expression that could represent the total cost of the nuts is:

C: \( 4.75(20 - x) \)

Summary

• Question 1 answer: C: \( 20 - x \)
• Question 2 answer: C: \( 4.75(20 - x) \)