Answer:
[tex]n = 65m[/tex]
Number of minutes is 80 minutes
Step-by-step explanation:
Given
The attached table
Calculating the number of copies the machine can make in a minute
Represent number of minutes with m and number of copies with n
First, we need to calculate the ratio of m to n
[tex]Ratio = \frac{n}{m}[/tex]
When m = 5; n = 325
[tex]Ratio = \frac{325}{5}[/tex]
[tex]Ratio = 65[/tex]
When m = 10; n = 650
[tex]Ratio = \frac{650}{10}[/tex]
[tex]Ratio = 65[/tex]
When m = 15; n = 975
[tex]Ratio = \frac{975}{15}[/tex]
[tex]Ratio = 65[/tex]
When we continue for other values of m and n, the ratio remains the same;
So; we make use of [tex]Ratio = \frac{n}{m}[/tex] to determine the relationship between m and n
Substitute 65 for Ratio
[tex]65 = \frac{n}{m}[/tex]
Multiply both sides by m
[tex]m * 65 = \frac{n}{m} * m[/tex]
[tex]65m = n[/tex]
[tex]n = 65m[/tex]
This implies that, you have to multiply the number of minutes by 65 to get the number of copies
Calculating the number of minutes to print 5200 copies;
In this case;
Ratio = 65 and n = 5200
So;
[tex]Ratio = \frac{n}{m}[/tex] becomes
[tex]65 = \frac{5200}{m}[/tex]
Multiply both sides by m
[tex]65 * m = \frac{5200}{m} * m[/tex]
[tex]65 * m = 5200[/tex]
Divide both sides by 65
[tex]\frac{65 * m}{65} = \frac{5200}{65}[/tex]
[tex]m = \frac{5200}{65}[/tex]
[tex]m = 80[/tex]
Hence; number of minutes is 80 minutes
