Type the correct answer in each box.
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 1/2
the number of type A cabinets produced. The number of type C cabinets produced was 20 more than 3/2
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 _
.
Type A cabinets produced:
Total number of cabinets produced:
Let's solve the problem step by step.
Step 1: Assign variables
Let's call the number of type A cabinets produced as "x".
Step 2: Calculate the number of type B cabinets produced
According to the given information, the number of type B cabinets produced was 30 more than 1/2 the number of type A cabinets produced.
So, the number of type B cabinets produced = (1/2)x + 30.
Step 3: Calculate the number of type C cabinets produced
According to the given information, the number of type C cabinets produced was 20 more than 3/2 times the number of type A cabinets produced.
So, the number of type C cabinets produced = (3/2)x + 20.
Step 4: Set up the equation for the same number of type B and type C cabinets
According to the given information, the company made the same number of type B and type C cabinets last week. So, we can set up the equation:
(number of type B cabinets) = (number of type C cabinets)
(1/2)x + 30 = (3/2)x + 20
Step 5: Solve the equation
To solve the equation, let's isolate x on one side:
(1/2)x - (3/2)x = 20 - 30
-(1/2)x = -10
x = (-10) / (-(1/2))
x = 20
So, the number of type A cabinets produced was 20.
Step 6: Calculate the total number of cabinets produced
To calculate the total number of cabinets produced, we need to sum up the number of each type of cabinet produced:
Total number of cabinets = (number of type A cabinets) + (number of type B cabinets) + (number of type C cabinets)
Total number of cabinets = 20 + ((1/2)(20) + 30) + ((3/2)(20) + 20)
Total number of cabinets = 20 + 10 + 30 + 30 + 20
Total number of cabinets = 110
So, the total number of cabinets produced last week was 110.