Question

1. gabriel needs 4 cups of apples for 3 pies. how many cups of apples does he need for 9 pies?

solution:
set up a proportion relating cups of apples to pies
\\(\frac{cups\\ of\\ apples}{pies}\\ \frac{4}{3} = \frac{x}{9}\\) \quad cross multiply and solve for \\(x\\).
\\(x = \frac{4\times9}{3} = 12\\) \quad for 9 pies we need 12 cups of apple.

1. if the ratio of blue marbles to red marbles is 3:2 and there are 18 blue marbles, how many red marbles are there?
2. the ratio of cats to dogs in a shelter is 5:4. if there are 20 dogs, how many cats are there?
3. the ratio of chocolate bars to candy packets is 3:1. if there are 15 candy packets, how many chocolate bars are there?
4. a recipe calls for 2 cups of flour for every 3 cups of sugar. if you have 12 cups of sugar, how many cups of flour do you need?
5. the ratio of apples to oranges in a basket is 4:5. if there are 45 oranges, how many apples are there?
6. in a school, the ratio of teachers to students is 1:25. if there are 15 teachers, how many students are there?

Explanation:

1) Step1: Set up proportion for marbles

Let $x$ = red marbles. $\frac{3}{2} = \frac{18}{x}$

1) Step2: Cross multiply to solve $x$

$x = \frac{18 \times 2}{3} = 12$

2) Step1: Set up proportion for animals

Let $x$ = cats. $\frac{5}{4} = \frac{x}{20}$

2) Step2: Cross multiply to solve $x$

$x = \frac{5 \times 20}{4} = 25$

3) Step1: Set up proportion for treats

Let $x$ = chocolate bars. $\frac{3}{1} = \frac{x}{15}$

3) Step2: Solve for $x$

$x = 3 \times 15 = 45$

4) Step1: Set up proportion for ingredients

Let $x$ = flour cups. $\frac{2}{3} = \frac{x}{12}$

4) Step2: Cross multiply to solve $x$

$x = \frac{2 \times 12}{3} = 8$

5) Step1: Set up proportion for fruits

Let $x$ = apples. $\frac{4}{5} = \frac{x}{45}$

5) Step2: Cross multiply to solve $x$

$x = \frac{4 \times 45}{5} = 36$

6) Step1: Set up proportion for school

Let $x$ = students. $\frac{1}{25} = \frac{15}{x}$

6) Step2: Cross multiply to solve $x$

$x = 15 \times 25 = 375$

Answer:

1. 12 red marbles
2. 25 cats
3. 45 chocolate bars
4. 8 cups of flour
5. 36 apples
6. 375 students