If the cupcakes cost twice as much as the brownies and I sold 12 brownies and 8 cupcakes totally $63 how much did I sell each for

Question

If the cupcakes cost twice as much as the brownies and I sold 12 brownies and 8 cupcakes totally $63 how much did I sell each for

Answer 1

63= 12x +8x

Brownie=2Cupcake

So if brownie is x

Cupcake is 2x,

Now solve

63= 12x +8x2

63= 12x +16x

63= 28x

x=63/28 = 2.25

Now plug back into second equation:

63=12(2.25) + 16(2.25)

63= 27 + 36

So you sold 12 brownies at the total sale of $27

And 16 cupcakes at the total sale of $36

Both totaling to $63.

Answer 2

In order to answer this question, you need to write a couple of equations (two of them because there are two things you want to find out: the price of the cupcakes, and the price of the brownies). But what should you write? The best way to discover this is to play around with the problem.

For example, imagine that both the cupcakes and the brownies cost $1 each. How much money would you have made then? Well, you sold 12 brownies, so that's 12x$1=$12, and 8 cupcakes, so that's 8x$1=$8. You got $12 for brownies and $8 from the cupcakes, so you got $12+$8=$20 total. Clearly this is not the correct answer, since you know you made $63, but that's OK. We're not trying to guess the answer. We're only trying to get a feel for the problem.

Let's try it again, but assigning different prices to the baked goods. Let's say the brownies cost $2 each, and the cupcakes still $1. So now you'd make: 12 brownies x $2 each + 8 cupcakes x $1 each = $24 from the brownies + $8 from the cupcakes = $32 total.

Hopefully by now you're seeing the pattern. Let's say now that the brownies cost $B each, and the cupcakes $C each. Then you would make 12 x $B + 8 x $C from selling everything. You know that you made $63, so we have the first equation:

12 B + 8 C = 63

Since this equation has two unknowns, we can't solve it as is. But the problem gives us some more information. It also says the "cupcakes cost twice as much as the brownies". That is $C is twice $B. Or, in equation form:

C = 2 B

We can now use this second equation to solve the first one. Wherever we see C, we will replace it and write 2B instead, since the second equations says they're the same thing. So:

12 B + 8 (2 B) = 63 or

12 B + 16 B = 63

Now your equation has just one unknown, so we can solve it just fine. Once you know the value of B (that is, the price of the brownies), you will also know the price of the cupcakes, since it's double the price of the brownies.

After you have your answer, you should check that it makes sense by simply adding up your profits and making sure it does all add up to $63.

Answer 3

12b + 8c = 63

c=2b

12b +8(2b) = 63

12b+16b = 63

28b = 63

b = 63/28 = $2.25 per brownie

c= 2(63/28)= 63/14 = $4.50 per cupcake

check the answers

12(2.25) + 8(4.5)

= 27+36=63

Answer 4

b represents price of brownies

2b repesents pice of cupcakes

12b + 8(2b) = 63

Can you solve for b and answer?