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 2 times the number of type A cabinets produced. The number of type C cabinets produced was 6 more than 6 times the number of type A cabinets produced. The company made the same number of type B and type C cabinets. Let x represent the number of type A cabinets.

Answer 1

The number of type A cabinets produced is 6.

Step-by-step explanation:

We are given that the number of type B cabinets produced last week was 30 more than 2 times the number of type A cabinets produced. Let's represent the number of type A cabinets as x. Therefore, the number of type B cabinets would be 2x + 30. We are also given that the number of type C cabinets produced was 6 more than 6 times the number of type A cabinets produced, which can be represented as 6x + 6. Finally, the company made the same number of type B and type C cabinets, so we can set up the equation 2x + 30 = 6x + 6 to find the value of x.

Combining like terms and solving this equation, we get 4x = 24 and x = 6. Therefore, the number of type A cabinets produced is 6.