To solve the equation [tex]\(\frac{2}{5}(y+10) = 8\)[/tex], let's break down the steps to find the value of [tex]\(y\)[/tex].
1. Start with the given equation:
[tex]\[
\frac{2}{5}(y+10) = 8
\][/tex]
2. Isolate the term [tex]\((y + 10)\)[/tex]:
Multiply both sides of the equation by the reciprocal of [tex]\(\frac{2}{5}\)[/tex], which is [tex]\(\frac{5}{2}\)[/tex], to eliminate the fraction.
[tex]\[
(y + 10) = 8 \times \frac{5}{2}
\][/tex]
3. Perform the multiplication on the right-hand side:
[tex]\[
(y + 10) = 8 \times \frac{5}{2}
\][/tex]
Simplify the multiplication:
[tex]\[
(y + 10) = \frac{40}{2}
\][/tex]
[tex]\[
(y + 10) = 20
\][/tex]
4. Solve for [tex]\(y\)[/tex]:
Subtract 10 from both sides to isolate [tex]\(y\)[/tex].
[tex]\[
y = 20 - 10
\][/tex]
[tex]\[
y = 10
\][/tex]
Therefore, the solution to [tex]\(\frac{2}{5}(y+10) = 8\)[/tex] is [tex]\(\boxed{10}\)[/tex]. The correct answer is B) 10.
