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Hoang has worked as a nurse at Springfield General Hospital for 7 years longer than her friend Bill. Two years ago, she had been
at the hospital for twice as long. How long has each been at the hospital?

Respuesta :

MrRoyal

Answer:

[tex]Bill\to 9\ years[/tex]

[tex]H \to 16\ years[/tex]

Step-by-step explanation:

Let

[tex]H \to Hoang[/tex]

[tex]B \to Bill[/tex]

Currently:

[tex]H = B + 7[/tex]

Two years ago

[tex]H - 2 = 2 * (B -2)[/tex]

Required

H and B

We have:

[tex]H - 2 = 2 * (B -2)[/tex]

Open bracket

[tex]H -2 =2B - 4[/tex]

Add 2 to both sides

[tex]H -2+2 =2B - 4+2[/tex]

[tex]H =2B -2[/tex]

Substitute [tex]H = B + 7[/tex]

[tex]B + 7 =2B -2[/tex]

Collect like terms

[tex]2B - B =7+2[/tex]

[tex]B = 9[/tex]

Substitute [tex]B = 9[/tex] in [tex]H = B + 7[/tex]

[tex]H = B + 7[/tex]

[tex]H = 9 + 7[/tex]

[tex]H = 16[/tex]