Question

the arithmetic mean of 25, 29, and x is 29. find x. answer: x =

Explanation:

Step1: Recall mean formula

The formula for the arithmetic mean of a set of numbers $a_1,a_2,\cdots,a_n$ is $\bar{a}=\frac{a_1 + a_2+\cdots+a_n}{n}$. Here, $n = 3$, $a_1=25$, $a_2 = 29$, $a_3=x$ and $\bar{a}=29$. So we have the equation $\frac{25 + 29+x}{3}=29$.

Step2: Multiply both sides by 3

Multiply both sides of the equation $\frac{25 + 29+x}{3}=29$ by 3 to get $25+29 + x=29\times3$.

Step3: Simplify the right - hand side

Calculate $29\times3 = 87$, so the equation becomes $25+29+x=87$.

Step4: Combine like terms on the left - hand side

$25 + 29=54$, so the equation is $54+x=87$.

Step5: Solve for x

Subtract 54 from both sides of the equation $54+x=87$: $x=87 - 54$.

Answer:

$x = 33$