Answer:
5 cakes and 9 pies
Explanation:
Let's assume the baker made x cakes and y pies.
Since she used 1 cup of flour for each cake, the total flour used for cakes would be x cups.
Similarly, since she used 3/4 cup of flour for each pie, the total flour used for pies would be (3/4)y cups.
According to the information given, the total desserts made were 14, so we can set up the following equation:
x + y = 14
Also, the total flour used was 11 3/4 cups, which can be written as 11.75 cups:
x + (3/4)y = 11.75
Now, we can solve these two equations simultaneously to find the values of x (cakes) and y (pies):
x + y = 14
x + (3/4)y = 11.75
Subtract equation 2 from equation 1 to eliminate x:
(x + y) - (x + (3/4)y) = 14 - 11.75
y - (3/4)y = 2.25
Now, combine like terms:
(1 - 3/4)y = 2.25
(1/4)y = 2.25
Next, isolate y by dividing both sides by 1/4:
y = 2.25 ÷ (1/4)
y = 2.25 × 4
y = 9
Now that we have the value of y (pies), we can find the value of x (cakes) by substituting y back into one of the original equations:
x + y = 14
x + 9 = 14
Subtract 9 from both sides to isolate x:
x = 14 - 9
x = 5
So, the baker made 5 cakes and 9 pies.