Use the situation below for both parts of the question.

Question

Aunt Sally is pricing cakes for a school dance. She wants one large cake and some cupcakes.

Dolphin Bake Shop charges $2 for each cupcake, plus $43 for the large cake. This is represented by the equation T = 2c + 43, where c is the number of cupcakes and T is the total cost.

Make A Splash Bakery charges $33 for the large cake and $3 for each cupcake. This is represented by the equation T = 3c + 33, where c is the number of cupcakes and T is the total cost.

Part 1

Aunt Sally wants to know for how many cupcakes would the cost for the two options be the same.



Responses

10 cupcakes
10 cupcakes

2 cupcakes
2 cupcakes

3 cupcakes
3 cupcakes

0 cupcakes
0 cupcakes
Question 2
Part 2
In the solution, the x-value represents the
Choose...
and the y-value represents the
Choose...
when the cost is the same at both shops.

Answer 1

To find out for how many cupcakes the cost for the two options would be the same, we need to set the two equations equal to each other:

1. Dolphin Bake Shop:
   \[ T = 2c + 43 \]

2. Make A Splash Bakery:
   \[ T = 3c + 33 \]

Setting the two equations equal to each other:

\[ 2c + 43 = 3c + 33 \]

Next, we'll solve for \( c \):

1. Subtract \( 2c \) from both sides:
   \[ 43 = c + 33 \]

2. Subtract \( 33 \) from both sides:
   \[ 10 = c \]

So, the cost for both options will be the same when Aunt Sally orders 10 cupcakes.

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Question 2, Part 2:

In the solution, the x-value represents the number of cupcakes and the y-value represents the total cost when the cost is the same at both shops.