Question

Karen is replacing an old water storage tank on her farm with two smaller tanks that together have the same storage capacity as the old tank. The capacity of the old tank, in gallons, can be represented by the function T(x) = 250x + 4.5, where x is the storage capacity of a bucket, in gallons, that Karen uses on the farm. The capacity, in gallons, of one of the new, smaller tanks can be represented by the function S(x) = 150x + 3.2.

The function which best describes C(x), the capacity, in gallons, of the other smaller tank is C(x) = x +

Answer 1

`C(x)=100x+1.3`

Explanation:

we have

T(x) -----> the capacity of the old tank, in gallons

S(x) ----> the capacity, in gallons, of one of the new, smaller tanks

C(x) ----> the capacity, in gallons, of the other of the new, smaller tanks

x ----> the storage capacity of a bucket, in gallons

we know that

`T(x)=S(x)+C(x)` ------> equation A

`T(x) = 250x + 4.5` ----> equation B

`S(x) = 150x + 3.2` ----> equation C

Substitute the equation B and equation C in equation A and solve for C(x)

`250x + 4.5= 150x + 3.2+C(x)`

`(250x-150x) + (4.5-3.2)= C(x)`

`(100x) + (1.3)= C(x)`

Rewrite

`C(x)=100x+1.3`