Ratio Problem-Solving - Pre Algebra

1. A recipe that serves 4 uses 6 eggs. How many eggs are needed to serve 10 at the same ratio?

   15 eggs. Each serving uses $\frac{6}{4} = 1.5$ eggs, and $1.5 \times 10 = 15$.

2. In a ratio problem that gives the total, what does dividing the total by the sum of the ratio terms give?

   The value of one part. Multiply it by each ratio term to find each quantity.

3. Paint is mixed blue to yellow in a $2:5$ ratio. How many liters of blue go with 10 liters of yellow?

   4 liters. Yellow is multiplied by 2 (5 to 10), so blue is $2 \times 2 = 4$.

4. A recipe uses flour and sugar in a $3:1$ ratio. How many cups of sugar go with 12 cups of flour?

   4 cups. The flour is multiplied by 4 (3 to 12), so the sugar is too: $1 \times 4 = 4$.

5. Two numbers are in a $5:3$ ratio and add to 64. What is the larger number?

   40. There are 8 parts, each worth $64 \div 8 = 8$, so the larger is $5 \times 8 = 40$.

6. A drink is mixed juice to water in a $1:4$ ratio, making 15 cups in all. How many cups are water?

   12 cups. There are 5 parts of 3 cups each, and water is 4 parts.

7. Two quantities are in the ratio $a:b$. What fraction of the total is the first quantity?

   $\frac{a}{a + b}$. The total has $a + b$ equal parts, and the first quantity is $a$ of them.

8. Red to blue marbles are in a $4:7$ ratio, and there are 12 more blue marbles than red. How many red marbles are there?

   16. The difference is 3 parts, so one part is $12 \div 3 = 4$ and red is $4 \times 4 = 16$.

9. If $A:B = 2:3$ and $B:C = 3:4$, what is $A:C$ in simplest form?

   $1:2$. Since $B$ is 3 in both, $A:B:C = 2:3:4$, and $2:4 = 1:2$.

10. Cats to dogs at a shelter are in a $3:5$ ratio, and there are 15 dogs. How many cats and dogs are there in all?

    24. One part is $15 \div 5 = 3$, so there are $3 \times 3 = 9$ cats and $9 + 15 = 24$ animals.

11. The ratio of boys to girls in a class is $2:3$, and there are 30 students. How many girls are there?

    18. There are 5 parts, each worth $30 \div 5 = 6$, so girls are $3 \times 6 = 18$.

12. When a recipe is scaled up or down, what must be done to every ingredient amount?

    Multiply every amount by the same scale factor. This keeps all the ratios between ingredients equal.

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