Before you read

Answer first — the lesson below explains it.

At a community food bank, the ratio of volunteers to families served is $1 : 15$ . During a holiday drive, 480 families are served. How many volunteers are working?

A
30
B
32
C
36
D
48

Check your answer

Answer:

Before you read

Answer first — the lesson below explains it.

A craft store mixes two types of beads—glass and wooden—in the ratio $3 : 7$ . If a jewelry kit contains 50 beads total, how many glass beads are included?

A
15
B
21
C
25
D
35

Check your answer

Answer:

Theory

What Is a Ratio?

A ratio compares two quantities. If a class has 12 boys and 18 girls, the ratio of boys to girls is $12:18$ , which simplifies to $2:3$ .

A proportion is an equation stating that two ratios are equal:
$\frac{a}{b} = \frac{c}{d}$

Ratios remain constant in proportional relationships

To solve a proportion, cross-multiply: $a \cdot d = b \cdot c$ .

$\frac{2}{5} = \frac{x}{20}$
$5x = 40$ cross multiply
$x = 8$

Solving a proportion using cross multiplication

Example 1

A recipe calls for 3 cups of flour for every 2 cups of sugar. If you use 9 cups of flour, how many cups of sugar do you need?

Set up the proportion: $\frac{3}{2} = \frac{9}{x}$

Cross-multiply: $3x = 18$

Divide both sides by 3: $x = 6$

x = 6

cups of sugar

Example 2

The ratio of cats to dogs at a shelter is $5:3$ . If there are 40 cats, how many dogs are there?

Set up the proportion: $\frac{5}{3} = \frac{40}{x}$

Cross-multiply: $5x = 120$

Divide: $x = 24$

x = 24

dogs

Quick check

You just read it. Can you apply it?

A shipping warehouse stores small, medium, and large packages in the ratio $5 : 2 : 1$ . If there are 120 packages in total, how many medium packages are there?

A
15
B
24
C
30
D
75

Check your answer

Answer:

Total parts: $5 + 2 + 1 = 8$ . Each part: $\frac{120}{8} = 15$ . Medium packages: $2 \times 15 = 30$ .

Theory

Part-to-Part vs. Part-to-Whole

Part-to-Part ratio: compares one part to another part. Example: boys to girls = $2:3$ .

Part-to-Whole ratio: compares one part to the total. Example: boys to total = $2:5$ (since $2 + 3 = 5$ ).

The SAT often requires you to convert between these two types.

Example 1

In a bag of 40 marbles, the ratio of red to blue marbles is $3:5$ . How many red marbles are there?

Total parts: $3 + 5 = 8$

Each part represents: $\frac{40}{8} = 5$ marbles

Red marbles: $3 \times 5 = 15$

15 red marbles

Quick check

You just read it. Can you apply it?

At a local gym, the ratio of male to female members is $4 : 5$ . After a promotional campaign, 8 more women sign up and the ratio becomes $4 : 7$ . How many male members does the gym have?

A
12
B
16
C
20
D
24

Check your answer

Answer:

Let males $= 4 k$ , original females $= 5 k$ . After 8 more females: $\frac{4 k}{5 k + 8} = \frac{4}{7}$ . Cross-multiply: $28 k = 20 k + 32$ . So $8 k = 32$ , $k = 4$ . Males $= 4 \times 4 = 16$ .

Common Mistakes

Common Mistakes to Avoid

Mixing up order

The ratio of A to B is $\frac{A}{B}$ , not $\frac{B}{A}$ . Read carefully!

Remember: avoid this error.

Confusing part-to-part with part-to-whole

If the ratio of boys to girls is $2:3$ , the fraction of boys is $\frac{2}{5}$ , not $\frac{2}{3}$ .

Remember: confusing part-to-part with part-to-whole — If the ratio of boys to girls is

2:3

, the fraction of boys is

\frac{2}{5}

, n...

Not simplifying

Always check if the ratio can be reduced. $12:18 = 2:3$ .

Remember: avoid this error.

Quick check

You just read it. Can you apply it?

A bakery uses flour and sugar in the ratio $\frac{x}{y} = \frac{3}{4}$ . If the bakery uses a total of $x + y = 35$ cups, what is the value of $x$ ?

A
12
B
15
C
20
D
21

Check your answer

Answer:

From the ratio, $x = 3 k$ and $y = 4 k$ . Then $3 k + 4 k = 35$ , so $7 k = 35$ , $k = 5$ . Therefore $x = 3 \times 5 = 15$ .

Strategy

SAT Pro Tip

When the SAT gives you a ratio like $a:b:c$ , the total parts are $a + b + c$ . If the total quantity is $T$ , each part equals $\frac{T}{a+b+c}$ . This shortcut saves 20+ seconds on ratio problems.

After reading

Same question as before. What do you say now?

At a community food bank, the ratio of volunteers to families served is $1 : 15$ . During a holiday drive, 480 families are served. How many volunteers are working?

A
30
B
32
C
36
D
48

Check your answer

Answer:

Set up the proportion: $\frac{1}{15} = \frac{x}{480}$ . Cross-multiply: $15 x = 480$ . Divide: $x = 32$ .

After reading

Same question as before. What do you say now?

A craft store mixes two types of beads—glass and wooden—in the ratio $3 : 7$ . If a jewelry kit contains 50 beads total, how many glass beads are included?

A
15
B
21
C
25
D
35

Check your answer

Answer:

Total parts: $3 + 7 = 10$ . Glass beads: $\frac{3}{10} \times 50 = 15$ .

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