Aunt Martina is pricing cakes for a baby shower she is throwing. She wants one large cake shaped like a duckling and also some cupcakes in pastel colors. Sparrowtown Bakery charges $2 for each cupcake, plus $50 for the large cake. Dakota's Sweet Shoppe charges $44 for the large cake and $4 for each cupcake. If Aunt Martina orders a certain number of cupcakes, the cost will be the same at either bakery. What would the total cost be? How many cupcakes would that include?

3 cupcakes

Total of $56

Step-by-step explanation:

First we would need to create an expression for the total of each bakery, which would be the following with x representing the number of cupcakes.

2x + 50

4x + 44

Since we know that the total for both bakeries was the same we can simply make the expressions equal to one another and solve for x.

2x + 50 = 4x + 44  ... subtract 2x on both sides

50 = 2x + 44  ... subtract 44 on both sides

6 = 2x   ... divide both sides by 2

3 = x

Finally, we can see that at 3 cupcakes the total for both bakeries will be the same and be a total of

2(3) + 50

6 + 50

$56

answer: (-8,4) are the coordinates of a

step-by-step explanation:

let the side of square abcd is x .

thus the area of square abcd is .

now, by the diagram area of triangle ead= 1/2 × ea × ad = 1/2 × ea × x

( because ad is the side of square)

and, according to the question,

the areas of square abcd and right ead are equal.

⇒

⇒ea=2x

thus, ea: ab=2: 1

therefore, point a divides line segment eb into the ratio 2: 1.

⇒ by sectional formula coordinates of a are,

=

=

=(-8, 4)

thus the coordinates of a are (-8,4)