Question

Eve and Julian are making their own pizzas. Eve's crust weighs 18 ounces, and Julian's crust weighs 12 ounces. After Eve adds 4 spoonfuls of tomato sauce to her pizza and Julian adds 8 spoonfuls to his, the two pizzas weigh the same.
Which equation can you use to find w, the weight of a spoonful of tomato sauce in ounces?
How much does a spoonful of tomato sauce weigh?
Simplify any fractions.
ounces

18+4w=12w+8 18+4w=12+8w

Answer 1

To find the appropriate equation for balancing the weights of Eve's and Julian's pizzas, let's analyze the situation:

1. **Eve's pizza weight**:
- Crust = 18 ounces
- Sauce = 4 spoonfuls of w ounces each = \(4w\) ounces
- Total weight = \(18 + 4w\)

2. **Julian's pizza weight**:
- Crust = 12 ounces
- Sauce = 8 spoonfuls of w ounces each = \(8w\) ounces
- Total weight = \(12 + 8w\)

Since we know the weights of the two pizzas are equal once the sauce is added, we can set up the equation:

\[
18 + 4w = 12 + 8w
\]

Now, we can solve for \(w\):

1. Start with the equation:
\[
18 + 4w = 12 + 8w
\]

2. Rearrange it:
\[
18 - 12 = 8w - 4w
\]
This simplifies to:
\[
6 = 4w
\]

3. Divide both sides by 4 to isolate \(w\):
\[
w = \frac{6}{4} = \frac{3}{2}
\]

So, \(w\), the weight of a spoonful of tomato sauce, is \(1.5\) ounces.

Thus, the final answer is:

\[
\text{A spoonful of tomato sauce weighs } 1.5 \text{ ounces.}
\]