Question

A company manufactures three types of cabinets, type A, type B, and type C.

Last week, the number of type B cabinets produced was 30 more than the number of types A cabinets produced. The number of type C cabinets produced was 20 more than times the number of types A cabinets produced.

If the company made the same number of type B and type C cabinets last week, then the number of types A cabinets produced was
. The total number of cabinets produced last week was
.

Answer 1

Using a system of equations, it is found that:

• The number of type A cabinets produced was 10.

• The total number of cabinets produced last week was 80.

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We are going to call x the number of type A cabinets, y the number of type B and z the number of type C.

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The number of type B was 30 more than 1/2 the number of type A, thus:

$\\ \\ \\ \\ y = 30 + \frac{x}{2}$

The number of type C was 20 more than 3/2 the number of type A, thus:

$\\ \\ \\ \\ \\ 20 + \frac{3x}{2}$

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Same number of type B and type C, thus:

$\\ \\ \\ \\ y = z \\ \\ \\ \\ 30 + \frac{x}{2} = 20 + \frac{3x}{2} \\ \\ \\ \\ \frac{2x}{2} = 10 \\ \\ \\ \\ x = 10$

For B and C:

$\\ \\ \\ \\ y = 30 + \frac{x}{2} \\ \\ \\ = 30 + \frac{10}{2} \\ \\ \\ = 35 \\ \\ \\ \\ again \: \: \\ \\ \\ \\ z = 20 + \frac{3x}{2} \\ \\ \\ = 20 + \frac{30}{2} \\ \\ \\ \\ = 35$

Thus, in total:

$\\ \\ \\ \\ 10 + 35 + 35 = 80$

The total number of cabinets produced last week was 80.

Answer 2

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