Question

Serenity weighs an apple, a pear, and an orange for a fruit tart she is baking. The apple and orange weigh 15 ounces together. The orange and the pear weigh 11 ounces together. The apple and the pear weigh 14 ounces together. How much does each fruit weigh?

Answer 1

Let's denote the weights of the apple, pear, and orange as follows:

- Let \( a \) be the weight of the apple (in ounces).
- Let \( p \) be the weight of the pear (in ounces).
- Let \( o \) be the weight of the orange (in ounces).

We can set up the following equations based on the information provided:

1. \( a + o = 15 \) (the apple and orange together weigh 15 ounces)
2. \( o + p = 11 \) (the orange and pear together weigh 11 ounces)
3. \( a + p = 14 \) (the apple and pear together weigh 14 ounces)

Now, we can solve this system of equations step-by-step.

From the first equation, we can express \( o \) in terms of \( a \):
\[
o = 15 - a
\]

Now, we can substitute this expression for \( o \) into the second equation:
\[
(15 - a) + p = 11
\]
Simplifying this gives:
\[
p = 11 - 15 + a
\]
\[
p = a - 4
\]

Next, we substitute the expression for \( p \) into the third equation:
\[
a + (a - 4) = 14
\]
Simplifying this gives:
\[
2a - 4 = 14
\]
\[
2a = 18
\]
\[
a = 9
\]

Now that we have \( a \) (the weight of the apple), we can find \( o \) and \( p \).

Substituting \( a = 9 \) back into the equation for \( o \):
\[
o = 15 - a = 15 - 9 = 6
\]

And substituting \( a = 9 \) into the equation for \( p \):
\[
p = a - 4 = 9 - 4 = 5
\]

Thus, we have the weights of each fruit:

- The weight of the apple (\( a \)) is \( 9 \) ounces.
- The weight of the pear (\( p \)) is \( 5 \) ounces.
- The weight of the orange (\( o \)) is \( 6 \) ounces.

Final weights:
- Apple: 9 ounces
- Pear: 5 ounces
- Orange: 6 ounces