−6∣x−2∣−9=4∣x−2∣+5 what are the solutions of the following equations?

getting home from trick or treat celia and emma counted their candies. half of celias candies is equal to 2/3 of emmas candies.

blagie [28]

Candies with celias and emmas is 60 and 45 respectively.

Solution:

Given, Getting home from trick or treat celia and emma counted their candies. Half of celias candies is equal to 2/3 of emmas candies.

They had a total of 105 candies altogether.

We have to find how many candies did each of them have.

Let the number of candies with celias be n, then number of candies with emma will be 105 – n.

Now according to given condition.

$\begin{array}{l}{\frac{1}{2} \times \text { celias candies count }=\frac{2}{3} \times \text { emmas candies count }} \\\\ {\rightarrow \frac{1}{2} \times n=\frac{2}{3} \times(105-n)} \\\\ {\rightarrow 3 \times n=2 \times 2 \times(105-n)} \\\\ {\rightarrow 3 \times n=2 \times 2 \times(105-n)} \\\\ {\rightarrow 3 n=4(105-n)} \\\\ {\quad \rightarrow 3 n=420-4 n} \\\\ {\rightarrow 3 n=420-4 n} \\\\ {\rightarrow 3 n+4 n=420} \\\\ {\rightarrow 7 n=7 \times 60} \\\\ {\rightarrow n=60}\end{array}$