Question

for his science fair project, bryan is comparing slime recipes. for one batch, he weighs out $9\frac{3}{4}$ ounces of liquid starch and mixes it with 2 bottles of glue. for the other batch, he weighs out $7\frac{3}{4}$ ounces of liquid starch and mixes it with $2\frac{1}{2}$ 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?\
$9.75 - 2w = 7.75 - 2.5w$\
$9.75 + 2w = 7.75 + 2.5w$\
how much does a bottle of glue weigh?\
simplify any fractions.\
ounces

Explanation:

Step1: Identify the correct equation

The first batch has \( 9\frac{3}{4} \) ounces of liquid starch (which is \( 9.75 \)) and 2 bottles of glue (so \( 2w \)). The second batch has \( 7\frac{3}{4} \) ounces of liquid starch (which is \( 7.75 \)) and \( 2\frac{1}{2} \) bottles of glue (which is \( 2.5w \)). Since both batches weigh the same, the equation is \( 9.75 + 2w = 7.75 + 2.5w \).

Step2: Solve for \( w \)

Subtract \( 2w \) from both sides:
\( 9.75 = 7.75 + 0.5w \)
Subtract \( 7.75 \) from both sides:
\( 9.75 - 7.75 = 0.5w \)
\( 2 = 0.5w \)
Divide both sides by \( 0.5 \):
\( w = \frac{2}{0.5} = 4 \)

Answer:

The weight of a bottle of glue is \( \boldsymbol{4} \) ounces.