Question

Milan puts 1/4 of her lawn-mowing money in savings and uses 1/2 of the remaining money to pay back her sister. if she has $15 left, how much did she have at first?

Answer 1

Milan has 3/4 of her money left after spending it. She uses half the remaining money to pay back her sister so she has the other half of the remaining money left which is $15. Hence, amount of money left after saving= 15×2 =$30, which is 3/4 of the total initial amount. Hence initial amount = 30× (4/3) = $40

Answer 2

Milan had $40 at first.

Further Explanation

Given:

• Milan puts 1/4 of her lawn-mowing money in savings
• She uses 1/2 of the remaining money to pay back her sister
• She has $15 left

Question:

How much did she have at first?

Let's say, the money Milan's has at first is N

She puts 1/4 of her lawn-mowing money in savings, so it is  1/4N.

The remaining money is:

N- 1/4N = 3/4N

The next step, we are going to calculate the money to pay back her sister, which is 1/2 of the remaining money:

$\boxed {\frac{1}{2} \times \frac{3}{4} N = \frac{3}{8}N }$

So we can write the total money Milan had at first

= money for saving+ money for paying back + the amount of money left

$\boxed {N = \frac{1}{4}N + \frac{3}{8} N + 15 }\\ \boxed {N - \frac{1}{4}N - \frac{3}{8}N = 15 }$

To solve this equation, we need to find the common denominator for 4 and 8 which is 8:

$\boxed { \frac{8N-2N-3N}{8} = 15 }\\\boxed {\frac{3}{8}N = 15 }\\ \boxed {N = \frac{15 \times8}{3} = 40 }$

That's the money Milan had at first which is $40.

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Keywords: fraction, fraction additional, fraction multiplication, mixed fraction, division