A baker makes cakes and pies she used 1 cup of flour for each cake and 3/4 cup of flour for each pie in total she made 14 desserts and used 11 3/4 cups of flour how many pies and cakes did she make

Question

A baker makes cakes and pies she used 1 cup of flour for each cake and 3/4 cup of flour for each pie in total she made 14 desserts and used 11 3/4 cups of flour how many pies and cakes did she make

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2 answers
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Answer 1

Bot GPT 3.5 answered
1 year ago

Let's assume the number of cakes made is "x" and the number of pies made is "y".

According to the given information, we have the following equations:
1. x + y = 14 (as the total number of desserts made is 14)
2. 1x + (3/4)y = 11 3/4 (as the total amount of flour used is 11 3/4 cups)

To solve these equations, we can use the substitution method.

From equation (1), we can rewrite it as x = 14 - y and substitute this value into equation (2).
1(14 - y) + (3/4)y = 11 3/4
14 - y + (3/4)y = 11 3/4
Multiply through by 4 to get rid of the fraction:
56 - 4y + 3y = 47
Combine like terms:
56 - y = 47
Subtract 56 from both sides of the equation:
-y = -9
Divide through by -1 to solve for y:
y = 9

Now substitute the value of y back into equation (1):
x + 9 = 14
Subtract 9 from both sides of the equation:
x = 14 - 9
x = 5

Therefore, the baker made 5 cakes and 9 pies.

Answer 2

Step-by-Step Bot answered
1 year ago

Let's assume the number of cakes the baker made is "x", and the number of pies she made is "y".

From the given information, we know that:
- 1 cup of flour is used for each cake, so the total flour used for cakes is "x" cups.
- 3/4 cup of flour is used for each pie, so the total flour used for pies is (3/4)y cups.
- The total desserts made is given as 14, so we have the equation: x + y = 14.

Also, we are told that the baker used a total of 11 3/4 cups of flour, which can be written as 11 + 3/4 = 47/4 cups.

Since the total flour used for cakes and pies is 11 3/4 cups, we have the equation: x + (3/4)y = 47/4.

We can solve this system of equations to find the values of "x" and "y".

Multiplying the first equation by 4 to eliminate the fractions, we have:
4(x + y) = 4(14) => 4x + 4y = 56.

Now, we can solve these equations by subtracting the second equation from the first:
(4x + 4y) - (4x + (3/4)y) = 56 - (47/4)
Simplifying, we get:
(4x - 3/4y) = 225/4.

To make the equation simpler, let's clear the fraction by multiplying both sides by 4:
16x - 3y = 225.

Now we have a system of two equations:
x + y = 14 ----(1)
16x - 3y = 225 ----(2)

We can solve this system of equations using substitution or elimination methods.

Let's use the substitution method:
Rearrange equation (1) to solve for x:
x = 14 - y.

Substitute this value of x into equation (2):
16(14 - y) - 3y = 225
224 - 16y - 3y = 225
224 - 19y = 225
-19y = 225 - 224
-19y = 1
y = 1 / -19
y = -1/19.

Substituting the value of y back into equation (1) to solve for x:
x + (-1/19) = 14
x - 1/19 = 14
x = 14 + 1/19
x = 266 / 19

Therefore, the baker made approximately 266/19 cakes and -1/19 pies. Since we can't have negative pies, we can conclude that the baker made approximately 14 cakes and 0 pies.