Ratio Story Problems worksheet with five word problems requiring students to solve ratio-based scenarios.

Let's solve each problem step by step.

---

Problem 1:

The ratio of football players to basketball players in a school is 2:7. If there are 18 football players, how many basketball players are there?

#### Solution:
1. Let the number of football players be \(2x\) and the number of basketball players be \(7x\), where \(x\) is a common multiplier.
2. We are given that the number of football players is 18. Therefore:
\[
2x = 18
\]
3. Solve for \(x\):
\[
x = \frac{18}{2} = 9
\]
4. Now, find the number of basketball players:
\[
7x = 7 \times 9 = 63
\]

#### Answer:
\[
\boxed{63}
\]

---

Problem 2:

A recipe requires salt and sugar in the ratio of 2:3. If you are using 6 cups of salt, how many cups of sugar should you use?

#### Solution:
1. Let the amount of salt be \(2y\) and the amount of sugar be \(3y\), where \(y\) is a common multiplier.
2. We are given that the amount of salt is 6 cups. Therefore:
\[
2y = 6
\]
3. Solve for \(y\):
\[
y = \frac{6}{2} = 3
\]
4. Now, find the amount of sugar:
\[
3y = 3 \times 3 = 9
\]

#### Answer:
\[
\boxed{9}
\]

---

Problem 3:

Two numbers are in the ratio 5:6. If 2 is added to the first number and 3 is added to the second number, they are in the ratio 4:5. Find the numbers.

#### Solution:
1. Let the two numbers be \(5z\) and \(6z\), where \(z\) is a common multiplier.
2. According to the problem, when 2 is added to the first number and 3 is added to the second number, the new ratio becomes 4:5. Therefore:
\[
\frac{5z + 2}{6z + 3} = \frac{4}{5}
\]
3. Cross-multiply to solve for \(z\):
\[
5(5z + 2) = 4(6z + 3)
\]
4. Expand both sides:
\[
25z + 10 = 24z + 12
\]
5. Simplify by isolating \(z\):
\[
25z - 24z = 12 - 10
\]
\[
z = 2
\]
6. Now, find the original numbers:
\[
5z = 5 \times 2 = 10
\]
\[
6z = 6 \times 2 = 12
\]

#### Answer:
\[
\boxed{10 \text{ and } 12}
\]

---

Problem 4:

If a quantity is divided in the ratio 5:7 and the larger part is 84, find the total quantity.

#### Solution:
1. Let the two parts be \(5w\) and \(7w\), where \(w\) is a common multiplier.
2. We are given that the larger part is 84. Therefore:
\[
7w = 84
\]
3. Solve for \(w\):
\[
w = \frac{84}{7} = 12
\]
4. Now, find the total quantity:
\[
\text{Total quantity} = 5w + 7w = 12w = 12 \times 12 = 144
\]

#### Answer:
\[
\boxed{144}
\]

---

Problem 5:

Your recipe for chocolate chip cookies uses 1 cup of flour to make 12 cookies. How much flour will you need to make 20 cookies?

#### Solution:
1. The ratio of flour to cookies is \(1 \text{ cup} : 12 \text{ cookies}\).
2. Let \(x\) be the amount of flour needed for 20 cookies. Set up the proportion:
\[
\frac{1 \text{ cup}}{12 \text{ cookies}} = \frac{x \text{ cups}}{20 \text{ cookies}}
\]
3. Cross-multiply to solve for \(x\):
\[
1 \times 20 = 12 \times x
\]
\[
20 = 12x
\]
4. Solve for \(x\):
\[
x = \frac{20}{12} = \frac{5}{3} \approx 1.67 \text{ cups}
\]

#### Answer:
\[
\boxed{\frac{5}{3} \text{ or } 1.67}
\]

---

Final Answers:

1. \(\boxed{63}\)
2. \(\boxed{9}\)
3. \(\boxed{10 \text{ and } 12}\)
4. \(\boxed{144}\)
5. \(\boxed{\frac{5}{3} \text{ or } 1.67}\)