Sarah has $120 to spend on invitations and favors for a birthday party. The equation

Question

3x + 12y = 120 models the
combinations of invitations, x, and favors, y, for $120.
Part A
How many invitations can Sarah purchase if she does not buy any party favors?
Part B
How many party favors can Sarah purchase if she does not buy any invitations?

Answer 1

To solve the problem given the equation \(3x + 12y = 120\):

Part A

If Sarah does not buy any party favors, then \(y = 0\).

Substituting \(y = 0\) into the equation:

\[ 3x + 12(0) = 120 \]

This simplifies to:

\[ 3x = 120 \]

Next, solve for \(x\):

\[ x = \frac{120}{3} = 40 \]

So, Sarah can purchase 40 invitations if she does not buy any party favors.

Part B

If Sarah does not buy any invitations, then \(x = 0\).

Substituting \(x = 0\) into the equation:

\[ 3(0) + 12y = 120 \]

This simplifies to:

\[ 12y = 120 \]

Next, solve for \(y\):

\[ y = \frac{120}{12} = 10 \]

So, Sarah can purchase 10 party favors if she does not buy any invitations.

To summarize:

• Part A: 40 invitations
• Part B: 10 party favors