Last year Kate spent between 1/4 and 1/3

Sam Kinsman

Sure! Let's say Kate spent between 1/4 of her gross income on her mortgage payments, and we'll call her gross income x.

So we know that 1/4 of x was spent on her mortgage payments. So we can say:

1/4 * x = amount spent on mortgage payments

The problem tells us she spent $13,470 on mortgage payments, so:

1/4 * x = $13,470

Now, we want to solve for x, so we divide both sides by 1/4.

1/4 * x = $13,470
x = $13,470 / (1/4)

This becomes $13,470 * 4 = 53,880.

If you have a hard time seeing how we got $13,470 * 4, think of it this way:

x = $13,470 / (1/4)
x = $13,470 / (0.25) = 53,880

Finally, note that if we did $13,470 * 1/4, we would be calculating 1/4 of her mortgage payments. That's not what we want to do - we want to find 1/4 of her her income, and set that equal to her mortgage payments so we can find her income :)

I hope this helps! :)

Sep 12, 2017 • Reply

Alyaa Altabbaa

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Jun 24, 2015 • Reply

Jonathan , Magoosh Tutor

Hi Alyaa.

Kate spent $13,470 on her mortgage payments last year.
We are total that amount represents between 1/3 and 1/4 of her gross income.

The gross income is higher than the mortgage payments.

If (13,470) spent on mortgage payment is a SMALLER fraction of her income, then that means her INCOME is LARGER.

4 * (13,470) gives us her maximum possible gross income. In this case, (13,470) is 1/4 of the income.

3 * ( 13,470) ) gives us her minimum possible income. In this case, (13,470) is 1/3 of the income.

Hope that helps.

Jun 29, 2015 • Reply