Question

Hoang has been a nurse for 5 years longer than Bill. Three years ago she had been there twice as long? How long has each been there?
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Answer 1

Answer:

Bill: 8 years

Hoang: 13 years

Step-by-step explanation:

Let's say Hoang has been a nurse for H years and Bill has been a nurse for B years.

Hoang has been a nurse for 5 years longer than Bill. This means that B + 5 = H

Next, 3 years ago, she had been there twice as long.

(B-3) and (H-3) represent Bill and Hoang 3 years ago respectively.

(B-3) * 2 = (H-3)

We thus have two equations

B+5 = H

(B-3) * 2 = H-3

Substitute B+5 for H in the second equation

2*B - 6 = B+5-3

2B-6 = B+2

add 6 to both sides to put all the constants on one side

2B = B + 8

subtract B from both sides to isolate the variable

B = 8

H = B+5 = 13