Question

takes two scoops of detergent for every three scoops of fabric softener. if there are 28 scoops of detergent remaining, how many scoops of fabric softener will be needed?
what is the ratio of vowels to consonants?

Explanation:

First Sub - Question (Detergent and Fabric Softener)

Step1: Define the ratio

The ratio of detergent to fabric softener is \(2:3\). Let the number of scoops of fabric softener be \(x\). We can set up a proportion using the ratio: \(\frac{\text{detergent}}{\text{fabric softener}}=\frac{2}{3}\)

Step2: Substitute the known value

We know the number of scoops of detergent is 28. So we substitute into the proportion: \(\frac{28}{x}=\frac{2}{3}\)

Step3: Cross - multiply and solve for \(x\)

Cross - multiplying gives us \(2x = 28\times3\). First, calculate \(28\times3=84\). Then, divide both sides by 2: \(x=\frac{84}{2}=42\)

Second Sub - Question (Ratio of Vowels to Consonants in "MATHEMATICS")

Step1: Identify vowels and consonants in "MATHEMATICS"

The word "MATHEMATICS" has the letters: M, A, T, H, E, M, A, T, I, C, S. Vowels are A, E, A, I (so 4 vowels). Consonants are M, T, H, M, T, C, S (so 7 consonants).

Step2: Find the ratio

The ratio of vowels to consonants is the number of vowels divided by the number of consonants, which is \(4:7\)

Answer:

• For the detergent and fabric softener problem: 42 scoops of fabric softener are needed.
• For the ratio of vowels to consonants in "MATHEMATICS": The ratio of vowels to consonants is \(4:7\)