Question

rates/ratio/proportions
create and solve a question for each topic we learned

• part to part (lemonade)
• part to whole (lottery)
• ratio in survey (swimming /soccer)

Explanation:

Step1: Part to Part (Lemonade)

Let's create a problem: In a lemonade recipe, the ratio of lemon juice to water is 1:4. If we use 2 cups of lemon juice, how much water do we need?
To solve, set up the proportion $\frac{\text{lemon juice}}{\text{water}}=\frac{1}{4}=\frac{2}{x}$. Cross - multiply: $1\times x = 4\times2$, so $x = 8$.

Step2: Part to Whole (Lottery)

Problem: In a lottery, the ratio of winning tickets to total tickets is 1:100. If there are 5000 total tickets, how many are winning?
Set up $\frac{\text{winning}}{\text{total}}=\frac{1}{100}=\frac{x}{5000}$. Cross - multiply: $100x = 5000$, so $x = 50$.

Step3: Ratio in Survey (Swimming/Soccer)

Problem: In a survey of 50 students, the ratio of students who like swimming to those who like soccer is 3:2. How many like swimming?
Total parts: $3 + 2=5$. Each part: $\frac{50}{5}=10$. Number of swimming - lovers: $3\times10 = 30$.

Answer:

• Part to Part: Water needed is 8 cups.
• Part to Whole: Winning tickets are 50.
• Ratio in Survey: 30 students like swimming.