Solved on Jan 12, 2024

Find the value of $x$ if the numbers 13, 18, and $x$ have a mean of 18.

STEP 1

Assumptions
1. We have three numbers: $13$ , $18$ , and $x$ .
2. The mean (average) of these three numbers is given as $18$ .

STEP 2

The mean of a set of numbers is calculated by summing all the numbers and then dividing by the count of numbers.
$Mean = \frac{Sum\, of\, all\, numbers}{Count\, of\, numbers}$

STEP 3

We know the mean is $18$ , and we have three numbers, so the count of numbers is $3$ .
$18 = \frac{13 + 18 + x}{3}$

STEP 4

Multiply both sides of the equation by $3$ to isolate the sum on one side.
$18 \times 3 = 13 + 18 + x$

STEP 5

Calculate the left side of the equation.
$54 = 13 + 18 + x$

STEP 6

Combine the known numbers on the right side of the equation.
$54 = 31 + x$

STEP 7

Subtract $31$ from both sides of the equation to solve for $x$ .
$54 - 31 = x$

STEP 8

Calculate the value of $x$ .
$x = 54 - 31 = 23$
The value of $x$ is $23$ .

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Find the value of $x$ if the numbers 13, 18, and $x$ have a mean of 18.

STEP 1

Assumptions
1. We have three numbers: $13$ , $18$ , and $x$ .
2. The mean (average) of these three numbers is given as $18$ .

STEP 2

The mean of a set of numbers is calculated by summing all the numbers and then dividing by the count of numbers.
$Mean = \frac{Sum\, of\, all\, numbers}{Count\, of\, numbers}$

STEP 3

We know the mean is $18$ , and we have three numbers, so the count of numbers is $3$ .
$18 = \frac{13 + 18 + x}{3}$

STEP 4

Multiply both sides of the equation by $3$ to isolate the sum on one side.
$18 \times 3 = 13 + 18 + x$

STEP 5

Calculate the left side of the equation.
$54 = 13 + 18 + x$

STEP 6

Combine the known numbers on the right side of the equation.
$54 = 31 + x$

STEP 7

Subtract $31$ from both sides of the equation to solve for $x$ .
$54 - 31 = x$

STEP 8

Calculate the value of $x$ .
$x = 54 - 31 = 23$
The value of $x$ is $23$ .

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Find the value of xxx if the numbers 13, 18, and xxx have a mean of 18.

STEP 1

Assumptions1. We have three numbers: 131313, 181818, and xxx.2. The mean (average) of these three numbers is given as 181818.

STEP 2

The mean of a set of numbers is calculated by summing all the numbers and then dividing by the count of numbers.Mean=Sum of all numbersCount of numbersMean = \frac{Sum\, of\, all\, numbers}{Count\, of\, numbers}Mean=CountofnumbersSumofallnumbers​

STEP 3

We know the mean is 181818, and we have three numbers, so the count of numbers is 333.18=13+18+x318 = \frac{13 + 18 + x}{3}18=313+18+x​

STEP 4

Multiply both sides of the equation by 333 to isolate the sum on one side.18×3=13+18+x18 \times 3 = 13 + 18 + x18×3=13+18+x

STEP 5

Calculate the left side of the equation.54=13+18+x54 = 13 + 18 + x54=13+18+x

STEP 6

Combine the known numbers on the right side of the equation.54=31+x54 = 31 + x54=31+x

STEP 7

Subtract 313131 from both sides of the equation to solve for xxx.54−31=x54 - 31 = x54−31=x

STEP 8

Calculate the value of xxx.x=54−31=23x = 54 - 31 = 23x=54−31=23The value of xxx is 232323.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the value of $x$ if the numbers 13, 18, and $x$ have a mean of 18.

Assumptions
1. We have three numbers: $13$ , $18$ , and $x$ .
2. The mean (average) of these three numbers is given as $18$ .

The mean of a set of numbers is calculated by summing all the numbers and then dividing by the count of numbers.
$Mean = \frac{Sum\, of\, all\, numbers}{Count\, of\, numbers}$

We know the mean is $18$ , and we have three numbers, so the count of numbers is $3$ .
$18 = \frac{13 + 18 + x}{3}$

Multiply both sides of the equation by $3$ to isolate the sum on one side.
$18 \times 3 = 13 + 18 + x$

Calculate the left side of the equation.
$54 = 13 + 18 + x$

Combine the known numbers on the right side of the equation.
$54 = 31 + x$

Subtract $31$ from both sides of the equation to solve for $x$ .
$54 - 31 = x$

Calculate the value of $x$ .
$x = 54 - 31 = 23$
The value of $x$ is $23$ .