Respuesta :

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