Last year Kate spent between \(\frac{1}{4}\) and \(\frac{1}{3}\) of her gross income on her mortgage payments. If Kate spent $13,470 on her mortgage payments last year, which of the following could have been her gross income last year?

Indicate all such gross incomes.

A) $40,200
B) $43,350
C) $47,256
D) $51,996
E) $53,808
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Let's examine the two EXTREME cases
They are:
case i: Kate spent 1/3 of her gross income on her mortgage payments
case ii: Kate spent 1/4 of her gross income on her mortgage payments

case i: Kate spent 1/3 of her gross income on her mortgage payments
Let x = Kate's gross income last year
So, 1/3 of x = $13,470
In other words, x/3 = $13,470
Multiply both sides by 3 to get: x = $40,410


case ii: Kate spent 1/4 of her gross income on her mortgage payments
Let x = Kate's gross income last year
So, 1/4 of x = $13,470
In other words, x/4 = $13,470
Multiply both sides by 4 to get: x = $53,880

So, Kate's gross income must be BETWEEN $40,410 and $53,880

Answer: B, C, D, E

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

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