Ratio and proportion - direct proportion worksheet - Free Printable

Direct Proportion Worksheet Solutions

The worksheet involves solving problems using the concept of direct proportion. In direct proportion, as one quantity increases, the other quantity increases at the same rate (or vice versa). The relationship can be expressed as:

\[
\frac{a}{b} = \frac{c}{d}
\]

where \( a \) and \( b \) are related in the same way as \( c \) and \( d \).

Let's solve each problem step by step.

---

Problem 1:

A woman drinks 7 bottles of water in a day. How many bottles of water would she consume in 3 days?

#### Solution:
- Bottles of water consumed in 1 day = 7
- We need to find the number of bottles consumed in 3 days.
- Since the consumption is directly proportional to the number of days, we multiply the daily consumption by 3:

\[
7 \text{ bottles/day} \times 3 \text{ days} = 21 \text{ bottles}
\]

#### Answer:
\[
\boxed{21}
\]

---

Problem 2:

Suzie gets paid \$1600 for 2 hours of babysitting. How much pay should she get if she babysits for 5 hours?

#### Solution:
- Pay for 2 hours = \$1600
- We need to find the pay for 5 hours.
- First, calculate the hourly rate:
\[
\text{Hourly rate} = \frac{\$1600}{2 \text{ hours}} = \$800/\text{hour}
\]
- Now, calculate the pay for 5 hours:
\[
\$800/\text{hour} \times 5 \text{ hours} = \$4000
\]

#### Answer:
\[
\boxed{4000}
\]

---

Problem 3:

A cat eats off 6 cans of cat-food in 2 days. How much cat-food would the same cat consume in 3 days?

#### Solution:
- Cans of cat-food eaten in 2 days = 6
- We need to find the amount of cat-food eaten in 3 days.
- First, calculate the daily consumption:
\[
\text{Daily consumption} = \frac{6 \text{ cans}}{2 \text{ days}} = 3 \text{ cans/day}
\]
- Now, calculate the consumption for 3 days:
\[
3 \text{ cans/day} \times 3 \text{ days} = 9 \text{ cans}
\]

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

---

Problem 4:

Rita eats 2 slices of pizza for every can of soda drunk. If she drank 5 cans of soda, how many pizzas did she eat?

#### Solution:
- Pizza slices per can of soda = 2
- Cans of soda drunk = 5
- We need to find the total number of pizza slices eaten.
- Since the number of pizza slices is directly proportional to the number of cans of soda, we multiply:

\[
2 \text{ slices/can} \times 5 \text{ cans} = 10 \text{ slices}
\]

#### Answer:
\[
\boxed{10}
\]

---

Problem 5:

Brian’s secretary said she uses 2 ink cartridges every 3 months to print reports. How many cartridges would she require over 9 months?

#### Solution:
- Ink cartridges used in 3 months = 2
- We need to find the number of cartridges used in 9 months.
- Since the usage is directly proportional to the time period, we first determine the monthly usage:
\[
\text{Monthly usage} = \frac{2 \text{ cartridges}}{3 \text{ months}} = \frac{2}{3} \text{ cartridges/month}
\]
- Now, calculate the usage for 9 months:
\[
\frac{2}{3} \text{ cartridges/month} \times 9 \text{ months} = 6 \text{ cartridges}
\]

#### Answer:
\[
\boxed{6}
\]

---

Final Answers:

1. \(\boxed{21}\)
2. \(\boxed{4000}\)
3. \(\boxed{9}\)
4. \(\boxed{10}\)
5. \(\boxed{6}\)

These solutions use the principle of direct proportion to relate the quantities in each problem. Each step ensures clarity and correctness.