Question

aruna had some cookies she gave 1/6 of cookies to her brother then she ate 18 cookies and gave 17 cookies to her mother she then had 1/4 of cookies left
(a) how many cookies did she have first
(b) what fraction of total cookies she ate

Answer 1

Answer:

(a) The number of cookies that she had at first is 60.

(b) The fraction of total cookies that she ate is 3/10

Step-by-step explanation:

Let's call the number of cookies Aruna had originally "x".

After giving 1/6 of her cookies to her brother, she had x - x/6 = 5x/6 cookies left.

After eating 18 cookies, she had 5x/6 - 18 = 5x/6 - 18 cookies left.

And after giving 17 cookies to her mother, she had 5x/6 - 18 - 17 = 5x/6 - 35 cookies left.

According to the problem, she had 1/4 of her original number of cookies left, so:

$\frac{5x}{6} -35 =\frac{x}{4} \\\\\frac{5x}{6} -\frac{x}{4} =35\\\\\frac{10x-3x}{12} =35\\\\\frac{7x}{12} = 35$

$x = \frac{35 * 12}{7} = 60$

Thus, x = 60

So Aruna had 60 cookies originally.

As for the second part of the question, the number of cookies Aruna ate was 18, and the total number of cookies she had originally was 60, so the fraction of the total cookies she ate is 18/60 which is 1/5.

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