Question

You found that in this system of equation, t = 9 when g = 12. What does this solution mean in the context of this problem?
3t+2g = 51
t = 21−g

g = 12
t = 9

The solution shows that the 21-pound order consisted of
pounds of trail mix and
pounds of granola.

Answer 1

To understand the problem, we have a system of equations that relates two variables: \( t \) (the weight of trail mix in pounds) and \( g \) (the weight of granola in pounds). The equations are given as follows:

1. \( 3t + 2g = 51 \)
2. \( t = 21 - g \)

The solution provided states that when \( g = 12 \), we find \( t = 9 \). Let's analyze what this means in the context of the problem.

Given that:

- \( g = 12 \) means there are 12 pounds of granola.
- \( t = 9 \) means there are 9 pounds of trail mix.

The total order weight is given by the equation \( t + g \):

\[
t + g = 9 + 12 = 21 \text{ pounds}
\]

Now, we can verify it meets the first equation:

Substituting \( t = 9 \) and \( g = 12 \) into the first equation:

\[
3(9) + 2(12) = 27 + 24 = 51
\]

This checks out correctly.

Thus, the solution indicates that in the 21-pound order, there are:

- **9 pounds of trail mix** (represented by \( t \))
- **12 pounds of granola** (represented by \( g \))

So, to fill in the blanks in the statement:

The solution shows that the 21-pound order consisted of **9 pounds of trail mix** and **12 pounds of granola**.