Question

Last Saturday, 46 kids took the SAT. The number of girls was 8 more than the number of boys. Define variables, write a system of equations to find the number of boys and the number of girls who took the SAT last Saturday and solve.

Answer 1

Let's define the variables:

- Let \( b \) represent the number of boys who took the SAT.
- Let \( g \) represent the number of girls who took the SAT.

We are given two pieces of information that can be converted into equations:

1. The total number of kids who took the SAT was 46:
\[
b + g = 46
\]

2. The number of girls was 8 more than the number of boys:
\[
g = b + 8
\]

Now we have the following system of equations:

\[
\begin{align*}
1. & \quad b + g = 46 \quad (1) \\
2. & \quad g = b + 8 \quad (2)
\end{align*}
\]

Now we can substitute equation (2) into equation (1):

Substituting \( g \) in equation (1):
\[
b + (b + 8) = 46
\]

Combining like terms:
\[
2b + 8 = 46
\]

Now, subtract 8 from both sides:
\[
2b = 38
\]

Next, divide by 2:
\[
b = 19
\]

Now that we have the number of boys, we can find the number of girls using equation (2):
\[
g = b + 8 = 19 + 8 = 27
\]

Thus, the solution is:
- Number of boys: \( 19 \)
- Number of girls: \( 27 \)

To summarize:
- There were **19 boys** and **27 girls** who took the SAT last Saturday.