Carcass wrote:

Each of the 576 houses in Tenantville is owned by one of the following landlords: Matt, Gavin, Angela, or Susan. Matt and Angela together own twice as many houses as Gavin and Susan own. If Gavin owns 100 more houses than Susan owns, and Matt owns 100 more houses than Angela owns, how many houses does Susan own?

A) 46

B) 142

C) 146

D) 192

E) 242

Since we're trying to determine the number of houses Susan owns, let's focus on her info first.

Gavin owns 100 more houses than Susan ownsLet

x = number of houses Susan owns

So,

x+100 = number of houses Gavin owns

Matt and Angela together own twice as many houses as Gavin and Susan ownSo, combined houses of Matt and Angela = 2(combined houses of Gavin and Susan)

We get: combined houses of Matt and Angela = 2(

x +

x+100)

Simplify: combined houses of Matt and Angela = 2(2x + 100)

Simplify: combined houses of Matt and Angela =

4x + 200Each of the 576 houses in Tenantville is owned by one of the following landlords: Matt, Gavin, Angela, or SusanSo, (# of Matt's houses) + (# of Angela's houses) + (# of Gavin's houses) + (# of Susan's houses) = 576

We can combine the first two values to get: (combined houses of Matt and Angela) + (# of Gavin's houses) + (# of Susan's houses) = 576

Substitute to get:

4x + 200 +

x+100 +

x = 576

Simplify: 6x + 300 = 576

Solve to get: x = 46

Answer:

Cheers,

Brent

_________________

Brent Hanneson – Creator of greenlighttestprep.com

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