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

Answer 1

To set up an equation, we can denote \( w \) as the weight of a spoonful of tomato sauce in ounces.

The total weight of Eve's pizza after she adds the tomato sauce can be represented as:
\[
18 + 4w
\]
where 18 ounces is the weight of her crust and \( 4w \) is the weight of the sauce.

The total weight of Julian's pizza after he adds the tomato sauce can be represented as:
\[
12 + 8w
\]
where 12 ounces is the weight of his crust and \( 8w \) is the weight of the sauce.

Since both pizzas weigh the same after the sauce is added, we can set up the following equation:
\[
18 + 4w = 12 + 8w
\]

Now, let's solve for \( w \):

1. Subtract \( 4w \) from both sides:
\[
18 = 12 + 4w
\]

2. Subtract 12 from both sides:
\[
6 = 4w
\]

3. Divide both sides by 4:
\[
w = \frac{6}{4} = \frac{3}{2} = 1.5
\]

Thus, the weight of a spoonful of tomato sauce is \( \boxed{1.5} \) ounces.