1. How much would a package with 18 slices cost at the same price per slice? Explain or show your reasoning. 2. A copy machine can print 480 copies every 4 minutes. a. How many cop... 1. How much would a package with 18 slices cost at the same price per slice? Explain or show your reasoning. 2. A copy machine can print 480 copies every 4 minutes. a. How many copies can it print in 10 minutes? b. A teacher printed 720 copies. How long did it take to print?
Understand the Problem
The question requires calculating the cost per slice of cheese in one problem and determining how many copies a machine can print in a given time period in another. The first part involves division and the second part involves multiplication and division.
Answer
The cost per slice of cheese is approximately $0.159$, the machine can print 1200 copies in 10 minutes, and it took 6 minutes to print 720 copies.
Answer for screen readers
-
The cost per slice of cheese is approximately $0.159$.
-
a. The machine can print 1200 copies in 10 minutes.
b. It took 6 minutes to print 720 copies.
Steps to Solve
- Calculate Cost Per Slice of Cheese
First, find the total number of slices in the package and the cost of the package:
- Cost of the package = $2.87
- Total slices = 18
Now, calculate the cost per slice using the formula:
$$ \text{Cost per slice} = \frac{\text{Total cost}}{\text{Number of slices}} = \frac{2.87}{18} $$
- Determine Copies in 10 Minutes (a)
Next, find out how many copies the machine can print in 10 minutes. Given that it prints 480 copies every 4 minutes, we first determine the copies printed in 1 minute:
$$ \text{Copies per minute} = \frac{480 \text{ copies}}{4 \text{ minutes}} = 120 \text{ copies/minute} $$
Now, calculate the total copies in 10 minutes:
$$ \text{Copies in 10 minutes} = \text{Copies per minute} \times 10 = 120 \times 10 $$
- Calculate Time Taken to Print 720 Copies (b)
To find out how long it took to print 720 copies, we again use the rate we calculated earlier (120 copies per minute). Set up the equation:
$$ \text{Time} = \frac{\text{Total copies}}{\text{Copies per minute}} = \frac{720}{120} $$
-
The cost per slice of cheese is approximately $0.159$.
-
a. The machine can print 1200 copies in 10 minutes.
b. It took 6 minutes to print 720 copies.
More Information
- The cost per slice reflects the per-unit price of the cheese, useful for budgeting.
- The calculation of copies and time helps understand machine efficiency and planning workloads in an office setting.
Tips
- Miscalculating the cost per slice by forgetting to divide by the total number of slices.
- Confusing the time taken with the rate of printing; it's crucial to remember that rates are typically per minute when calculating total time for multiple copies.
AI-generated content may contain errors. Please verify critical information
