Question

Write and solve an equation to find the value of the variable.

5.2, 8.3, 8.5, 7.7, 7.8 , y ; mean = 7.1



5.1


5.8


3.9


5.3

Answer 1

To find the value of \( y \) when the mean of the numbers is given, we can use the formula for the mean:

\[
\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}
\]

Here, we have the values: \( 5.2, 8.3, 8.5, 7.7, 7.8, y \).

The mean is given as \( 7.1 \) and the total number of values is \( 6 \).

We can set up the equation:

\[
7.1 = \frac{5.2 + 8.3 + 8.5 + 7.7 + 7.8 + y}{6}
\]

Now, we calculate the sum of the known values:

\[
5.2 + 8.3 + 8.5 + 7.7 + 7.8 = 37.5
\]

Substituting this into the equation gives us:

\[
7.1 = \frac{37.5 + y}{6}
\]

Now, multiply both sides by \( 6 \):

\[
7.1 \times 6 = 37.5 + y
\]

Calculating \( 7.1 \times 6 \):

\[
42.6 = 37.5 + y
\]

Next, subtract \( 37.5 \) from both sides to solve for \( y \):

\[
y = 42.6 - 37.5
\]

Calculating the right side:

\[
y = 5.1
\]

Thus, the value of \( y \) is \( \boxed{5.1} \).