Question

For his science fair project, Bryan is comparing slime recipes. For one batch, he weighs out 9
3
4
ounces of liquid starch and mixes it with 2 bottles of glue. For the other batch, he weighs out 7
3
4
ounces of liquid starch and mixes it with 2
1
2
bottles of glue. Both batches end up weighing the same amount.
Which equation can you use to find w, the weight of a bottle of glue in ounces?
How much does a bottle of glue weigh?
Simplify any fractions.

Answer 1

To solve the problem, let's first express the total weight of each batch in terms of \( w \), the weight of a bottle of glue in ounces.

For the first batch:
- The weight of liquid starch = \( 9 \frac{3}{4} \) ounces = \( \frac{39}{4} \) ounces (since \( 9 \frac{3}{4} = 9 + \frac{3}{4} = \frac{36}{4} + \frac{3}{4} = \frac{39}{4} \))
- The weight from 2 bottles of glue = \( 2w \)

The total weight of the first batch is:
\[
\frac{39}{4} + 2w
\]

For the second batch:
- The weight of liquid starch = \( 7 \frac{3}{4} \) ounces = \( \frac{31}{4} \) ounces (since \( 7 \frac{3}{4} = 7 + \frac{3}{4} = \frac{28}{4} + \frac{3}{4} = \frac{31}{4} \))
- The weight from \( 2 \frac{1}{2} \) bottles of glue (which is \( \frac{5}{2} \) bottles) = \( \frac{5}{2}w \)

The total weight of the second batch is:
\[
\frac{31}{4} + \frac{5}{2}w
\]

Since both batches weigh the same, we set the equations equal to each other:
\[
\frac{39}{4} + 2w = \frac{31}{4} + \frac{5}{2}w
\]

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

First, let's eliminate the fractions by multiplying the entire equation by 4:
\[
4 \left( \frac{39}{4} + 2w \right) = 4 \left( \frac{31}{4} + \frac{5}{2}w \right)
\]
This gives:
\[
39 + 8w = 31 + 10w
\]

Now, isolate \( w \):
\[
39 - 31 = 10w - 8w
\]
\[
8 = 2w
\]
\[
w = 4
\]

Thus, the weight of one bottle of glue is **4 ounces**.

To summarize:
1. The equation to use is given by \(\frac{39}{4} + 2w = \frac{31}{4} + \frac{5}{2}w\).
2. A bottle of glue weighs **4 ounces**.