Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Jada and her friend Laura are each baking apple pies and tarts for a bake sale, using the same recipes. Jada baked 8 apple pies and 1 apple tart, using a total of 70 apples. Laura made 3 apple pies and 5 apple tarts, which used 54 apples. How many apples does each dessert require?

An apple pie uses
apples and an apple tart requires
apples.

Answer 1

To set up a system of equations for the problem, we can define:

- Let \( p \) be the number of apples needed for one apple pie.
- Let \( t \) be the number of apples needed for one apple tart.

Now we can create equations based on the information given:

For Jada:
- She baked 8 apple pies and 1 apple tart, which used a total of 70 apples. This gives us our first equation:
\[
8p + 1t = 70 \tag{1}
\]

For Laura:
- She made 3 apple pies and 5 apple tarts, which used a total of 54 apples. This gives us our second equation:
\[
3p + 5t = 54 \tag{2}
\]

Now we have the following system of equations:

1. \( 8p + t = 70 \)
2. \( 3p + 5t = 54 \)

Next, we can solve this system using substitution or elimination. Let's use substitution with the first equation. From equation (1), we can express \( t \) in terms of \( p \):
\[
t = 70 - 8p \tag{3}
\]

Now, substitute equation (3) into equation (2):
\[
3p + 5(70 - 8p) = 54
\]

Distribute \( 5 \) in the equation:
\[
3p + 350 - 40p = 54
\]

Combine like terms:
\[
-37p + 350 = 54
\]

Subtract 350 from both sides:
\[
-37p = 54 - 350
\]
\[
-37p = -296
\]

Now, divide by -37:
\[
p = \frac{296}{37} = 8
\]

So, each apple pie requires \( 8 \) apples.

Next, we substitute \( p \) back into equation (3) to find \( t \):
\[
t = 70 - 8(8)
\]
\[
t = 70 - 64
\]
\[
t = 6
\]

Thus, each apple tart requires \( 6 \) apples.

Summarizing our results, we have:

An apple pie uses **8** apples and an apple tart requires **6** apples.