Question

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 1

Answer:

Step-by-step explanation

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

Answer 2

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

Let :

• Number of machines = m
• Number of nails produced = n
• Time taken = t

Using Principle of variation :

• Number of machines α nails produced α 1/time

• $m = \frac{kn}{t}$ ; where k = constant of proportionality

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:

$m = \frac{\frac{25}{9}n}{t}$

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

$1 = \frac{\frac{25}{9}n}{60}$

$60 = \frac{{25}{9}}{n}$

Divide both sides by 25/9 to isolate n

$60 \times \frac{9}{25} = n$

$n = \frac{540}{25} = 21 \frac{3}{5} \: thousand \: nails$

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