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For his science fair project, Bryan is comparing slime recipes. For one batch, he weighs out ounces of liquid starch and mixes it with bottles of glue. For the other batch, he weighs out ounces of liquid starch and mixes it with bottles of glue. Both batches end up weighing the same amount.Which equation can you use to find , the weight of a bottle of glue in ounces?Choices:(A) (B) How much does a bottle of glue weigh?Simplify any fractions. ounces
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Q. For his science fair project, Bryan is comparing slime recipes. For one batch, he weighs out ounces of liquid starch and mixes it with bottles of glue. For the other batch, he weighs out ounces of liquid starch and mixes it with bottles of glue. Both batches end up weighing the same amount.Which equation can you use to find , the weight of a bottle of glue in ounces?Choices:(A) (B) How much does a bottle of glue weigh?Simplify any fractions. ounces
- Denote weight of glue: Let's denote the weight of a bottle of glue as . Since both batches weigh the same amount, the total weight of the liquid starch and glue in each batch should be equal. For the first batch, the weight is the sum of the weight of the liquid starch and the weight of the two bottles of glue. For the second batch, it's the sum of the weight of the liquid starch and the weight of the two and a half bottles of glue. We can set up an equation to represent this situation.
- Set up equation: The equation should reflect the total weight of each batch being equal. For the first batch, we have ounces of liquid starch plus the weight of bottles of glue, which is . For the second batch, we have ounces of liquid starch plus the weight of bottles of glue, which is . The equation should be:
- Convert to fractions: First, we need to convert the mixed numbers to improper fractions to make the calculation easier. ounces is the same as ounces, and ounces is the same as ounces. Now we can rewrite the equation using these fractions:$(\frac{\(39\)}{\(4\)}) + \(2\)w = (\frac{\(31\)}{\(4\)}) + \(2\).\(5\)w
- Rearrange equation: To solve for \(w\), we need to get all the \(w\) terms on one side and the constants on the other. Let's subtract \(2w\) from both sides to move the \(w\) terms to the right side of the equation:\(\newline\)\((\frac{39}{4}) = (\frac{31}{4}) + 2.5w - 2w\)
- Combine like terms: Simplify the equation by combining like terms: \(\frac{39}{4} = \frac{31}{4} + 0.5w\)
- Isolate variable: Now, let's isolate \(w\) by multiplying both sides by \(2\) to get rid of the fraction: \(2 \times \left(\frac{39}{4}\right) = 2 \times \left(\frac{31}{4}\right) + w\)
- Perform multiplication: Perform the multiplication: \((\frac{78}{4}) = (\frac{62}{4}) + w\)
- Simplify fractions: Simplify the fractions by dividing both the numerator and the denominator by \(4\): \(19.5 = 15.5 + w\)
- Subtract to solve: Finally, subtract \(15.5\) from both sides to solve for \(w\): \(\newline\)\[w = 19.5 - 15.5\]
- Calculate difference: Calculate the difference: \(w = 4\)
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