Find value of x in the following equation?

Question

5+x+(5+x)*.15 = 25

I can do this in an excel using 4 columns but need to find a formula for it. Take 4 columns in an excel sheet and put 5 in first columns and 25 in 4th column. Second column formula is =D1-A1-C1 and third column is =(A1+B1)*0.15.

Answer 1

You have $1\cdot(5+x)+0.15\cdot(5+x) = 25$. Collecting the $(5+x)$ terms gives $$(1+0.15)(5+x)=25,$$ so $1.15(5+x)=25$.

Now divide both sides by $1.15$, then subtract $5$ from both sides.

Answer 2

Use the following rules:

• $(a+b)\cdot c = ac + bc$
• $a+b=c$ is the same as $a=b-c$

to change the equation into $$A\cdot x = B$$

for some two values of $x$.

Then, use the fact that

• If $a\neq 0$, then $a\cdot b = c$ is the same as $b=\frac{c}{a}$

to calculate $x$.