Question

A patient's hospice stay cost one-fourth as much as his visit to the emergency room. His home nursing cost twice as much as his hospice stay. If his total health care bill was $140,000, how much did his home nursing cost?

Answer 1

Let E, H and N represent the costs of Emergency room, Hospice stay and Nursing costs respectively.
H = 1/4 * E
N = 2 * H
E + H + N = 140,000

Three equations, three unknowns. Need to solve for N.

Answer 2

I can get as far as this, but then I am unfamiliar with how to do the math to complete the problem:

E + 1/4E + 2 1/4E = 140,000

How do I combine these "E" terms on the left?

Answer 3

E + 1/4 * E + 2 * 1/4 * E = 140,000
E * ( 1 + 1/4 + 1/2 ) = 140,000
E * ( 4/4 + 1/4 + 2/4) = 140,000
E * 7/4 = 140,000
E = 140,000 * 4 / 7 = 80,000
H = 1/4 * E = 1/4 * 80,000 = 20,000
N = 2 * H = 2 * 20,000 = $40,000

Answer 4

on line 3, where did "2/4" come from?

Answer 5

I know it is equivalent to 1/2, but where does the 1/2 originally come from?

Answer 6

Look at the 3rd term in the equation you derived. 2 * 1/4 * E is simplified to 1/2 * E.

Answer 7

The way you have written the third term looks like "two and a quarter" but ut should be "two times quarter times E".

Answer 8

ohhhhh, I was looking at it as a mixed number and not 2*1/4. OK, Thank you very much!

Answer 9

You are welcome.