Question

Write and solve an equation and then check your answer. Complete the statements.

Graciella divided her grapes equally among 6 friends. If each friend received 16 grapes, how many grapes did Graciella have?

(5 points)

The variable g represents? Response area.

The equation that correctly models the problem is? Response area.

To solve the equation for g,? Response area, on both sides of the equation.

The solution of the equation is? Response area.

Check the solution by substituting? Response area, for g and simplifying.

fill in the blank

Answer 1

Let's go through the problem step by step and fill in the required statements.

1. **The variable g represents?**
**Response area:** The total number of grapes Graciella had.

2. **The equation that correctly models the problem is?**
**Response area:** \( g = 6 \times 16 \)

3. **To solve the equation for g,?**
**Response area:** Multiply 6 by 16 on both sides of the equation.

4. **The solution of the equation is?**
**Response area:** \( g = 96 \)

5. **Check the solution by substituting?**
**Response area:** 96 for g and simplifying.

Now let's check the solution:

If we substitute \( g = 96 \) into the equation, we check:

\[
g = 6 \times 16
\]

Substituting \( g \):

\[
96 = 6 \times 16
\]

Calculating the right side:

\[
6 \times 16 = 96
\]

Since both sides of the equation are equal, the solution is confirmed.

So the filled-in statements are:

1. **The variable g represents:** The total number of grapes Graciella had.
2. **The equation that correctly models the problem is:** \( g = 6 \times 16 \)
3. **To solve the equation for g:** Multiply 6 by 16 on both sides of the equation.
4. **The solution of the equation is:** \( g = 96 \)
5. **Check the solution by substituting:** 96 for g and simplifying.