Explanation

To determine Kate's possible gross incomes:
\(\frac{1}{4}\) of her gross income is 13,470
\(\frac{1}{4} (x) = 13470\) → \((4)\frac{1}{4}(x) = (4)13470\)→ \(x = 53,880\)

1/3 of her gross income is 13,470
\(\frac{1}{3} (x) = 13470\) → \((3)\frac{1}{3} (x) = (3)13470\) → \(x = 40,410\)

Kate's gross income falls between $40,410 and $53,880, so the last four answer choices B,C,D, E are correct.
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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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