To find out how much car wax Rosie would use to shine her entire car, we can start with the information given: she uses \( \frac{1}{4} \) bottle of car wax to shine \( \frac{2}{3} \) of her car.
We can set up a proportion to find the amount of car wax used for the entire car (which is 1 full car).
First, we want to determine how much car wax \( x \) she would use for the entire car:
\[ \frac{1}{4} \text{ (bottle)} \text{ corresponds to } \frac{2}{3} \text{ (of the car)} \]
To find \( x \), we can set up a ratio:
\[ \frac{1}{4} \text{ (bottle)} \text{ to } \frac{2}{3} \text{ (of the car)} = x \text{ (bottle)} \text{ to } 1 \text{ (full car)} \]
This can be expressed as:
\[ \frac{\frac{1}{4}}{\frac{2}{3}} = \frac{x}{1} \]
To solve for \( x \), we can cross-multiply:
\[ x = \frac{1}{4} \div \frac{2}{3} \]
To divide fractions, we multiply by the reciprocal:
\[ x = \frac{1}{4} \times \frac{3}{2} = \frac{3}{8} \]
So, Rosie would need \( \frac{3}{8} \) of a bottle of car wax to shine her entire car.
Next, for the unit rate:
The unit rate gives us the amount of car wax needed per full car. We found that Rosie uses \( \frac{3}{8} \) of a bottle for her entire car, which can also be expressed as:
- For 1 car: \( \frac{3}{8} \) bottle
- For \( \frac{2}{3} \) of a car: \( \frac{1}{4} \) bottle
To find the unit rate (bottle per car), we can see that she uses \( \frac{3}{8} \) bottle for 1 car:
\[ \text{Unit rate} = \frac{3}{8} \text{ bottle per car} \]
Thus, Rosie uses \( \frac{3}{8} \) of a bottle of car wax to shine her entire car, with a unit rate of \( \frac{3}{8} \) bottle per car.
9 answers