Question

Can someone please help explain how to do this word problem?
A corner store sells two kinds of baked goods: cakes and pies. A cake costs $5 and a pie costs $7. In one day, the store sold 15 baked goods for a total of $91. How many cakes did they sell?

Answer 1

Let c and p be the number of cakes and pies sold respectively.
Solve the following for c and p:

{5 c + 7 p = 91, c + p = 15}

{c = 7, p = 8}

Answer 2

so i wanna plug in the c and p for the equation?

Answer 3

{5 c + 7 p = 91, c + p = 15} are two simultaneous equations to be solved for c and p. are you asking how to solve them for c and p or how they came about?

Answer 4

both i guess. lol

Answer 5

I get c+p=15 because 15 is how much goods they sold. But how would i figure out the equation to solve how many cakes they sold? 5 c + 7 p = 91 is this what i would use to solve for it?

Answer 6

Take the first equation. It says that the number of cakes sold times $5 plus the number of pies sold times $7 is equal to $91.

The next equation says that the sum of the number of pies and cakes sold is 15. All of the numbers come from the problem statement.

To solve equations for c and p, take the second equation and move c to the RHS.
p = 15 - c
Plug the symbolic value of p above into the first equation and solve for c.
5 c + 7 p = 91
5 c + 7 (15 - c) = 91
5 c + 105 - 7c = 91
-2c = -14
c = 7
Plug the numeric value of c, 7, into the revised version of the second equation and solve for p.
p = 15 - c
p = 15 - 7
p = 8

Answer 7

thank you for explaining it in details i think i kinda of got it.