Answer:
Hardware supplier will manufacture 60 Type A clamps, 180 Type B clamps and 150 Type C clamps.
Step-by-step explanation:
Given:
Company produces 3 types of clamp
Type A
Type B
Type C
production restrictions force it to make 10 more type C clamps in the total of the other types
Hence We can say that Clamp C is equal to sum of Clamp A and Clamp and 10
framing in equation form we get;
![C=A+B+10 \ \ \ \ \ equation \ 1](https://tex.z-dn.net/?f=C%3DA%2BB%2B10%20%5C%20%5C%20%5C%20%5C%20%5C%20equation%20%5C%201)
Also Given:
3 times as many Type B clamps as type A clamps
Hence we can say that Clamp B is equal to thrice of Clamp A.
![B=3A \ \ \ \ equation\ 2](https://tex.z-dn.net/?f=B%3D3A%20%5C%20%5C%20%5C%20%5C%20equation%5C%202)
Also Given
Total Number of Clamps = 490
Hence Total Number of Clamps is equal to sum of number of Clamps of Type A, Type B and Type C.
Framing in equation form we get;
![A+B+C =490 \ \ \ \ equation \ 3](https://tex.z-dn.net/?f=A%2BB%2BC%20%3D490%20%5C%20%5C%20%5C%20%5C%20equation%20%5C%203)
Substituting the equation 1 and Equation 2 in equation 3 we get
![A+B+C=490\\\\A+3A+A+B+10=490\\\\A+3A+A+3A+10=490\\\\8A = 490-10\\\\8A=480\\\\A=\frac{480}{8}=60](https://tex.z-dn.net/?f=A%2BB%2BC%3D490%5C%5C%5C%5CA%2B3A%2BA%2BB%2B10%3D490%5C%5C%5C%5CA%2B3A%2BA%2B3A%2B10%3D490%5C%5C%5C%5C8A%20%3D%20490-10%5C%5C%5C%5C8A%3D480%5C%5C%5C%5CA%3D%5Cfrac%7B480%7D%7B8%7D%3D60)
Now Substituting the Value of A in equation 2 we get;
![B=3A = 3\times60 =180](https://tex.z-dn.net/?f=B%3D3A%20%3D%203%5Ctimes60%20%3D180)
Now Substituting the values of A and B in equation 1 we get:
![C=A+B+10 = 60+180+10= 250](https://tex.z-dn.net/?f=C%3DA%2BB%2B10%20%3D%2060%2B180%2B10%3D%20250)
Now checking the same we get;
![A+B+C=490\\60+180+250=490\\490=490](https://tex.z-dn.net/?f=A%2BB%2BC%3D490%5C%5C60%2B180%2B250%3D490%5C%5C490%3D490)
Hence the Hardware supplier will manufacture 60 Type A clamps, 180 Type B clamps and 150 Type C clamps.