Grade 5 Word Problem Worksheet with four math word problems involving fractions, ratios, and real-life applications.

Let's solve each problem step by step.

---

Problem 1:

Tickets to the movies cost $24 for 1 adult. The price for 1 child was 2/3 of that price. How much did a family with 2 adults and 2 children have to pay?

#### Step-by-Step Solution:
1. Price for 1 adult: $24.
2. Price for 1 child:
\[
\text{Price for 1 child} = \frac{2}{3} \times 24 = \frac{2 \times 24}{3} = \frac{48}{3} = 16
\]
So, the price for 1 child is $16.
3. Total cost for 2 adults:
\[
\text{Cost for 2 adults} = 2 \times 24 = 48
\]
4. Total cost for 2 children:
\[
\text{Cost for 2 children} = 2 \times 16 = 32
\]
5. Total cost for the family:
\[
\text{Total cost} = \text{Cost for 2 adults} + \text{Cost for 2 children} = 48 + 32 = 80
\]

#### Final Answer:
\[
\boxed{80}
\]

---

Problem 2:

Mary earned $420 in May and only 5/7 of this in June. How much money did she earn in June?

#### Step-by-Step Solution:
1. Earnings in May: $420.
2. Earnings in June:
\[
\text{Earnings in June} = \frac{5}{7} \times 420 = \frac{5 \times 420}{7} = \frac{2100}{7} = 300
\]

#### Final Answer:
\[
\boxed{300}
\]

---

Problem 3:

Sam and Peter loved pizza. Peter ate \(1 \frac{1}{2}\) pizza and Sam ate \(4 \frac{2}{3}\) pizza over a 2-week period. How much pizza did they eat in that time?

#### Step-by-Step Solution:
1. Convert mixed numbers to improper fractions:
- Peter ate \(1 \frac{1}{2}\):
\[
1 \frac{1}{2} = \frac{2 \times 1 + 1}{2} = \frac{3}{2}
\]
- Sam ate \(4 \frac{2}{3}\):
\[
4 \frac{2}{3} = \frac{3 \times 4 + 2}{3} = \frac{12 + 2}{3} = \frac{14}{3}
\]
2. Add the amounts of pizza eaten by Peter and Sam:
\[
\text{Total pizza} = \frac{3}{2} + \frac{14}{3}
\]
3. Find a common denominator (the least common multiple of 2 and 3 is 6):
\[
\frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6}
\]
\[
\frac{14}{3} = \frac{14 \times 2}{3 \times 2} = \frac{28}{6}
\]
4. Add the fractions:
\[
\frac{9}{6} + \frac{28}{6} = \frac{9 + 28}{6} = \frac{37}{6}
\]
5. Convert the improper fraction back to a mixed number:
\[
\frac{37}{6} = 6 \frac{1}{6}
\]

#### Final Answer:
\[
\boxed{6 \frac{1}{6}}
\]

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Problem 4:

John and Allan started a business. In their first month they made $700. They decided to split the earnings in a ratio of 3:4, with Allan earning slightly more as he had invested more. How much did each of them earn?

#### Step-by-Step Solution:
1. Total earnings: $700.
2. Ratio of earnings: 3:4.
3. Sum of the parts of the ratio:
\[
3 + 4 = 7
\]
4. Value of one part:
\[
\text{Value of one part} = \frac{700}{7} = 100
\]
5. John's earnings (3 parts):
\[
\text{John's earnings} = 3 \times 100 = 300
\]
6. Allan's earnings (4 parts):
\[
\text{Allan's earnings} = 4 \times 100 = 400
\]

#### Final Answer:
\[
\boxed{300 \text{ and } 400}
\]

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Final Answers:

1. \(\boxed{80}\)
2. \(\boxed{300}\)
3. \(\boxed{6 \frac{1}{6}}\)
4. \(\boxed{300 \text{ and } 400}\)