or
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
Linda and her friend Valeria are each baking apple pies and tarts for a bake sale, using the same recipes. Linda baked 2 apple pies and 8 apple tarts, using a total of 44 apples. Valeria made 5 apple pies and 9 apple tarts, which used 66 apples. How many apples does each dessert require?
An apple pie uses
apples and an apple tart requires
apples.
Let's call the number of apples required for an apple pie "x" and the number of apples required for an apple tart "y".
Based on the information given, we can set up the following system of equations:
Equation 1: 2x + 8y = 44 (Linda's baking)
Equation 2: 5x + 9y = 66 (Valeria's baking)
We can solve this system of equations using any method, but for simplicity, we will use the substitution method.
From Equation 1, we can rearrange it to solve for x:
2x = 44 - 8y
x = (44 - 8y)/2
x = 22 - 4y
Now we substitute this expression for x into Equation 2:
5(22 - 4y) + 9y = 66
Expanding and simplifying:
110 - 20y + 9y = 66
-11y = -44
y = (-44)/(-11)
y = 4
Now substitute the value of y = 4 back into the expression for x:
x = 22 - 4y
x = 22 - 4(4)
x = 22 - 16
x = 6
Therefore, an apple pie requires 6 apples and an apple tart requires 4 apples.