A company manufactures three types of cabinets. It makes 110 cabinets each week. In the first week, the sum of the number of type-1 cabinets and twice the number of type-2 cabinets produced was 10 more than the number of type-3 cabinets produced. The next week, the number of type-1 cabinets produced was three times more than in the first week, no type-2 cabinets were produced, and the number of type-3 cabinets produced was the same as in the previous week.

Question

Jaida Mathis

Mathematics

8 February, 23:39

A company manufactures three types of cabinets. It makes 110 cabinets each week. In the first week, the sum of the number of type-1 cabinets and twice the number of type-2 cabinets produced was 10 more than the number of type-3 cabinets produced. The next week, the number of type-1 cabinets produced was three times more than in the first week, no type-2 cabinets were produced, and the number of type-3 cabinets produced was the same as in the previous week.

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Tate Macdonald · Answer 1

For the 1st week, let us find the numbers of the three types of cabinets to make it equivalent to 110, as the total number of cabinets produced each week.

Let's assume type-1 cabinets is x. The type-2 cabinets is 2x since it is stated that it is twice the number. And, type-3 cabinets will be (x+2x-10).

We'll come up with the formula below ...

total number of cabinets each week = type-1 cabinets + type-2 cabinets + type-3 cabinets

110 = x + 2x + (x + 2x-10) 110 = 3x + (3x-10) 110 = 6x - 10110+10 = 6x120 = 6x120/6 = x20 = x

For the second week using the equivalent of x:

type-1 cabinets = 3xtype-2 cabinets = 0type-3 cabinets = same as last week (50)

x=20

3x + (x+2x-10) = 1103 (20) + (20+40-10) = 11060 + 50 = 110110 = 110