Three machines are used to produce nails. the table displays the total number of nails produced by the three machines over different lengths of time

Answer:

Step-by-step explanation

they answer would be a whole number because you are multiplying by one thousand

Using the principle of proportionality, the number of nails that will be produced by 1 machine in 1 hour is [tex] 21 \frac{3}{5} \: thousand [/tex]

Let :

Using Principle of variation :

Using a row from the table :

t = 15 ; n = 81/5

3 = (81/5)k / 15

Cross multiply :

3 × 15 = (81/5)k

45 = (81/5)k

Divide both sides by (81/5) to isolate k

(45 ÷ 81/5) = k

k = (45 × 5/81) = 25/9 = 2.7777

Substituting the value of k into the expression:

[tex] m = \frac{\frac{25}{9}n}{t} [/tex]

We can use the expression to obtain, the value of n ; when m = 1 and t = (1 hour = 60 minutes)

[tex] 1 = \frac{\frac{25}{9}n}{60} [/tex]

[tex] 60 = \frac{{25}{9}}{n}[/tex]

Divide both sides by 25/9 to isolate n

[tex] 60 \times \frac{9}{25} = n [/tex]

[tex] n = \frac{540}{25} = 21 \frac{3}{5} \: thousand \: nails [/tex]

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