Starting with 113+ (2x+5)=180, combine like terms and to get 118+2x=180. Subtract 180-118, which gives you 62. Then you have 2x=62. Divide both sides by 2 to get a final answer of x=31.
Answer:
The formula to find the sum of the first n terms of our sequence is n divided by 2 times the sum of twice the beginning term, a, and the product of d, the common difference, and n minus 1. The n stands for the number of terms we are adding together.
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Candies with celias and emmas is 60 and 45 respectively.
<u>Solution:</u>
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}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%20%5Ctext%20%7B%20celias%20candies%20count%20%7D%3D%5Cfrac%7B2%7D%7B3%7D%20%5Ctimes%20%5Ctext%20%7B%20emmas%20candies%20count%20%7D%7D%20%5C%5C%5C%5C%20%7B%5Crightarrow%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%20n%3D%5Cfrac%7B2%7D%7B3%7D%20%5Ctimes%28105-n%29%7D%20%5C%5C%5C%5C%20%7B%5Crightarrow%203%20%5Ctimes%20n%3D2%20%5Ctimes%202%20%5Ctimes%28105-n%29%7D%20%5C%5C%5C%5C%20%7B%5Crightarrow%203%20%5Ctimes%20n%3D2%20%5Ctimes%202%20%5Ctimes%28105-n%29%7D%20%5C%5C%5C%5C%20%7B%5Crightarrow%203%20n%3D4%28105-n%29%7D%20%5C%5C%5C%5C%20%7B%5Cquad%20%5Crightarrow%203%20n%3D420-4%20n%7D%20%5C%5C%5C%5C%20%7B%5Crightarrow%203%20n%3D420-4%20n%7D%20%5C%5C%5C%5C%20%7B%5Crightarrow%203%20n%2B4%20n%3D420%7D%20%5C%5C%5C%5C%20%7B%5Crightarrow%207%20n%3D7%20%5Ctimes%2060%7D%20%5C%5C%5C%5C%20%7B%5Crightarrow%20n%3D60%7D%5Cend%7Barray%7D)
Hence, candies with celias and emmas is 60 and 45 respectively.