Acompany 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 .

Using a system of equations, it is found that:

----------------------------

----------------------------

----------------------------

----------------------------

Same number of type B and type C, thus:

The number of type A cabinets produced was 10.

----------------------------

For B and C:

Thus, in total:

The total number of cabinets produced last week was 80.

A similar problem is given at link

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

$450 i think. hope this ☺