Zara is creating slime for her science project. She uses 34 cups of glue for every 12 cup of water to make the perfect slime mixtureThe unit rate of cups of glue per cup of water in Zara's slime recipe is cup(s) of glue to cup(s) of water. b) If Zara needs to use 5 cups of water, how many cups of glue should she use to maintain the same ratio? cups of glue

Answer 1

To find the unit rate of cups of glue to cups of water in Zara's slime recipe, we divide the number of cups of glue by the number of cups of water:

\[ \text{Unit rate} = \frac{34 \text{ cups of glue}}{12 \text{ cups of water}} = \frac{34}{12} = \frac{17}{6} \approx 2.83 \text{ cups of glue per cup of water} \]

So, the unit rate is 17/6 cups of glue to 1 cup of water (or approximately 2.83 cups of glue for every 1 cup of water).

To find out how many cups of glue Zara should use for 5 cups of water while maintaining the same ratio, we can set up a proportion using the unit rate calculated.

Using the ratio found:

\[ \text{Cups of glue} = \left(\frac{34}{12}\right) \times \text{cups of water} \]

Substituting 5 cups of water:

\[ \text{Cups of glue} = \left(\frac{34}{12}\right) \times 5 = \frac{34 \times 5}{12} = \frac{170}{12} \]

Now, simplifying \(\frac{170}{12}\):

\[ \frac{170}{12} = \frac{85}{6} \approx 14.17 \text{ cups of glue} \]

Thus, Zara should use approximately 14.17 cups of glue to maintain the same ratio when using 5 cups of water.