Question

Complete the table below.
Number of pounds
Dollars per pound
Cost
​(in dollars)
x
18
  
18 x
y
  
6
  
6 y
90
  
10
  
900
​(Simplify your answers. Use integers or decimals for any numbers in the​ expression.)
Part 2
The person will need
  
enter your response here pounds of ​$18 coffee and
  
enter your response here pounds of ​$6 coffee.

Answer 1

To complete the table, we need to fill in the cost for each entry:

### Table Completion:

| Number of pounds | Dollars per pound | Cost (in dollars) |
|------------------|-------------------|----------------------|
| x | 18 | 18x |
| y | 6 | 6y |
| 90 | 10 | 900 |

### Finding x and y:

Let's assume that the total amount of coffee (pounds) needed is **90 pounds**, and the average cost given is $10 per pound.

To find how much of each type of coffee the person will need:

Let \( x \) be the pounds of $18 coffee and \( y \) be the pounds of $6 coffee. We have two conditions:
1. The total weight of the coffee:
\( x + y = 90 \)

2. The total cost of the coffee:
The average cost equation can be set up as:
\[
\frac{(18x + 6y)}{90} = 10
\]
Multiplying both sides by 90 gives:
\[
18x + 6y = 900
\]

### Solving the equations:

From the first equation:
\[
y = 90 - x
\]

Substituting \( y \) in the second equation:
\[
18x + 6(90 - x) = 900
\]

Expanding:
\[
18x + 540 - 6x = 900
\]
Combining like terms:
\[
12x + 540 = 900
\]
Subtracting 540 from both sides:
\[
12x = 360
\]
Dividing by 12:
\[
x = 30
\]

Substituting back for \( y \):
\[
y = 90 - 30 = 60
\]

### Final Answers:

- The person will need **30 pounds** of **$18 coffee**.
- The person will need **60 pounds** of **$6 coffee**.

### Filled Part 2:
- 30 pounds of $18 coffee
- 60 pounds of $6 coffee