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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)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
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.

g6=16g=2296multiply by 610the number of friend Graciella hasg=9622the number of grapes Graciella hadg+6=16divide by 6subtract 6the number of grades each of her friends hasg=10

1 answer

To solve the problem step-by-step, let's define the equation and work through it.

Let \( g \) represent the total number of grapes Graciella had.

  1. The equation that correctly models the problem: Graciella divided her grapes equally among 6 friends, and each friend received 16 grapes. This can be represented by the equation: \[ g = 6 \times 16 \]

  2. To solve the equation for \( g \), we multiply: \[ g = 6 \times 16 \] \[ g = 96 \]

  3. The solution of the equation is: \[ g = 96 \]

  4. Check the solution by substituting \( g = 96 \) for \( g \) and simplifying: \[ \frac{g}{6} = \frac{96}{6} = 16 \] Each friend gets 16 grapes, which confirms that our solution is correct.

Now let's fill in the responses:

  • The variable \( g \) represents: the number of grapes Graciella had.

  • The equation that correctly models the problem is: \( g = 6 \times 16 \).

  • To solve the equation for \( g \), multiply by 6 on both sides of the equation.

  • The solution of the equation is: 96.

  • Check the solution by substituting: 96 for g and simplifying.

Thus, Graciella had 96 grapes.