Certainly! Let's break down the problem step by step to determine how many tablespoons of ground coffee are required for 3 cups of water.
1. Understanding the Given Ratios:
The coffee machine requires [tex]\( 1 \frac{1}{2} \)[/tex] tablespoons of ground coffee for [tex]\( \frac{3}{4} \)[/tex] cup of water.
- Converting [tex]\( 1 \frac{1}{2} \)[/tex] to an improper fraction or decimal, we get:
[tex]\( 1 \frac{1}{2} = 1 + \frac{1}{2} = 1.5 \)[/tex] tablespoons of coffee.
2. Determine the Coffee-Water Ratio:
- The amount of water used is [tex]\( \frac{3}{4} \)[/tex] cups.
- Therefore, the coffee-to-water ratio is [tex]\( 1.5 \)[/tex] tablespoons per [tex]\( \frac{3}{4} \)[/tex] cup of water.
3. Scaling Up to 3 Cups of Water:
- We need to find out how many times [tex]\( \frac{3}{4} \)[/tex] cup fits into 3 cups.
- To do this, we divide 3 cups by [tex]\( \frac{3}{4} \)[/tex] cup:
[tex]\[
\text{Number of ratios in 3 cups} = \frac{3}{ \frac{3}{4} } = 3 \div \frac{3}{4} = 3 \times \frac{4}{3} = 4
\][/tex]
Hence, there are 4 such ratios in 3 cups of water.
4. Calculate the Total Amount of Coffee:
- Since each [tex]\( \frac{3}{4} \)[/tex] cup of water requires 1.5 tablespoons of coffee, we multiply the number of ratios by the amount of coffee:
[tex]\[
\text{Total coffee required} = 4 \times 1.5 = 6
\][/tex]
Thus, if 3 cups of water are used, you will need 6 tablespoons of ground coffee.
