Question

Plz help

A corner store sells two kinds of baked goods: cakes and pies. A cake costs $5 and a pie costs $4. In one day, the store sold 10 baked goods for a total of $46.
a. Write a system of equations to represent this situation.

b. Show work, using substitution, to determine how many cakes were sold

Answer 1

a. Required system of equations is:

c+p = 10

5c+4p = 46

b. 6 cakes were sold

Explanation:

Let p be the number of pies and c be the number of cakes.

Then according to given statement " the store sold 10 baked goods"

`c+p = 10\ \ \ Eqn\ 1`

And

"A cake costs $5 and a pie costs $4"

`5c+4p = 46\ \ \ \ Eqn\ 2`

Using equation 1,

`c=10-p`

Putting this value of c in equation 2:

`5(10-p)+4p = 46\\50-5p+4p = 46\\-p = 46-50\\-p = -4\\p = 4`

Putting p = 4 in equation 1

`c+4 = 10\\c = 10-4\\c =6`

Hence,

a. Required system of equations is:

c+p = 10

5c+4p = 46

b. 6 cakes were sold