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 type A cabinets produced. The number of type C cabinets produced was 20 more than times the number of type A cabinets produced. If the company made the same number of type B and type C cabinets last week, then the number of type A cabinets produced was . The total number of cabinets produced last week was .

Answer 1

B = 1/2A + 30
C = 3/2A + 20
B = C

1/2A + 30 = 3/2A + 20
30 - 20 = 3/2A - 1/2A
10 = A

B = 1/2A + 30
B = 1/2(10) + 30
B = 5 + 30
B = 35

C = 3/2A + 20
C = 3/2(10) + 20
C = 15 + 20
C = 35

type A cabinets produced was 10
type B and type C cabinets produced were both 35

Answer 2

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:

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

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

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

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Same number of type B and type C, thus:

$y = z$

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

$\frac{2x}{2} = 10$

$x = 10$

The number of type A cabinets produced was 10.

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For B and C:

$y = 30 + \frac{x}{2} = 30 + \frac{10}{2} = 30 + 5 = 35$

$z = 20 + \frac{3x}{2} = 20 + \frac{30}{2} = 20 + 15 = 35$

Thus, in total:

$10 + 35 + 35 = 80$

The total number of cabinets produced last week was 80.

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