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
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.
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.