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:
-
The total weight of the coffee:
\( x + y = 90 \) -
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
1 answer