what is the answer to this question?

Question

Bill and Mary Ann went to the Viola bakery. Bill bought 4 danishes and 9 filled donuts for $16.54. Mary Ann bought 6 of each for ​$13.56. What is the price of each type of​ pastry?

Answer 1

4x+9y=16.54

6x+6y=13.56

Several ways to do this. One is to subtract one from the other after multiplying to cancel out one variable.

4x - 9y = 16.54

-(9x + 9y) = 13.56 * 1.5

-5x = -3.80

x = 0.76 hence danish costs 76 cents and the donut is $1.50

Answer 2

This question requires the use of a system of equations. I will use the variable A to represent danish price and B to represent donut price.

If Bill bought 4 danishes and 9 donuts for $16.54, his equation would look like this: 4A+9B = 16.54

If Ann bought 6 of each, her equation would look like this 6A+6B = 13.56

First, let us manipulate one of these equations to find A or B. In this case, I will use Bill's equation to find A:

4A+9B = 16.54

We move the 9B to the right side: 4A = 16.54 - 9B

Then we divide by 4 to isolate A: A = (16.54-9B)/4

Next, we need to plug this value of A into Ann's equation:

6((16.54-9B)/4) + 6B = 13.56

We distribute the 6: (99.24 - 54B)/4 + 6B = 13.56

We simplify by dividing by 4 and combine terms: 24.81-13.5B + 6B = 13. 56 -> 24.81 - 7.5B = 13.56

We swap our B term to the right and isolate it: 24.81 - 13.56 = 7.5B -> 11.25 = 7.5B

Solve for B: B = 1.5

Now we know that our donut price is $1.50.

We can plug the donut price back into one of our original equations to solve for the danish price. I will use Ann's equation again:

6A + 6(1.5) = 13.56

We simplify and isolate the A term: 6A + 9 = 13.56 -> 6A = 13.56 - 9 -> 6A = 4.56

Solve for A: A = .76.

Now we know that our danish price is $0.76.

We can check this by plugging the values we found for both pastries into either one of our equations.

Let me know if you have any questions!

Answer 3

Let D= Danishes and F=Filled donuts

Bill: 16.54=4D+9F

Mary Ann: 13.56=6D+6F

Now we have 2 equations with 2 unknowns. We can solve by substitution or elimination.

I will use the elimination method.

We can multiply the 1st equation by 6 and the 2nd equation by 4 so that when we subtract the two equations, we will eliminate the D variable.

6(16.54=4D+9F) >>> 99.24=24D+54F

4(13.56=6D+6F) >>> 54.24=24D+24F

Subtract the 2 equations: 45 = 30F

Divide both sides by 30 to solve for F.

F= 1.50

Now to solve for D, you can substitute 1.50 in for F in either of the two original equations:

16.54=4D+9(1.50)

16.54=4D +13.50. Subtract 13.50 from both sides

3.04=4D. Divide both sides by 4

D=.76