Linear-Equations-in-One-Variable-Word-Problems-Workbook-3 - Free Printable

Let's solve each problem step by step using linear equations.

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Problem 1:

Geeta bought six bananas for Rs. 14. How many bananas can Sunita buy if she has Rs. 7?

#### Solution:
1. First, find the cost of one banana.
\[
\text{Cost of one banana} = \frac{\text{Total cost}}{\text{Number of bananas}} = \frac{14}{6} = \frac{7}{3} \text{ Rs.}
\]
2. Now, determine how many bananas Sunita can buy with Rs. 7.
\[
\text{Number of bananas Sunita can buy} = \frac{\text{Amount Sunita has}}{\text{Cost of one banana}} = \frac{7}{\frac{7}{3}} = 7 \times \frac{3}{7} = 3
\]

Answer: Sunita can buy 3 bananas.

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Problem 2:

A frame is 18 in wide and 6 in tall. If it is reduced to a height of 1 in, then how wide will it be?

#### Solution:
1. The width and height of the frame are proportional. Let the new width be \( x \).
2. Set up the proportion:
\[
\frac{\text{Original width}}{\text{Original height}} = \frac{\text{New width}}{\text{New height}}
\]
\[
\frac{18}{6} = \frac{x}{1}
\]
3. Solve for \( x \):
\[
\frac{18}{6} = x \implies x = 3
\]

Answer: The new width will be 3 inches.

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Problem 3:

A rectangle is 1 in tall and 2 in wide. If it is enlarged to a width of 6 in, then how tall will it be?

#### Solution:
1. The width and height of the rectangle are proportional. Let the new height be \( y \).
2. Set up the proportion:
\[
\frac{\text{Original width}}{\text{Original height}} = \frac{\text{New width}}{\text{New height}}
\]
\[
\frac{2}{1} = \frac{6}{y}
\]
3. Solve for \( y \):
\[
2y = 6 \implies y = \frac{6}{2} = 3
\]

Answer: The new height will be 3 inches.

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Problem 4:

A triangle is 16 in tall and 8 in wide. If it is reduced to a width of 2 in, then how tall will it be?

#### Solution:
1. The width and height of the triangle are proportional. Let the new height be \( h \).
2. Set up the proportion:
\[
\frac{\text{Original width}}{\text{Original height}} = \frac{\text{New width}}{\text{New height}}
\]
\[
\frac{8}{16} = \frac{2}{h}
\]
3. Simplify the left side:
\[
\frac{1}{2} = \frac{2}{h}
\]
4. Solve for \( h \):
\[
h = 2 \times 2 = 4
\]

Answer: The new height will be 4 inches.

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Problem 5:

The money used in Tonga is called the Pa'anga. The exchange rate is $1 for every 2 Pa'anga. Find how many Pa'anga you would receive if you exchanged $10.

#### Solution:
1. The exchange rate is $1 = 2 \text{ Pa'anga}$. Therefore, for $10:
\[
\text{Pa'anga received} = 10 \times 2 = 20
\]

Answer: You would receive 20 Pa'anga.

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Problem 6:

The money used in Saudi Arabia is called the Riyal. The exchange rate is $1 for every 4 Riyals. Find how many dollars you would receive if you exchanged 20 Riyals.

#### Solution:
1. The exchange rate is $1 = 4 \text{ Riyals}$. Therefore, for 20 Riyals:
\[
\text{Dollars received} = \frac{20}{4} = 5
\]

Answer: You would receive $5.

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Problem 7:

The currency in Poland is the Zlotych. The exchange rate is approximately 3 Zlotych for every $1. At this rate, how many dollars would you get if you exchanged 15 Zlotych?

#### Solution:
1. The exchange rate is 3 Zlotych = $1. Therefore, for 15 Zlotych:
\[
\text{Dollars received} = \frac{15}{3} = 5
\]

Answer: You would receive $5.

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Problem 8:

The money used in Kuwait is called the Dinar. The exchange rate is 1 Dinar for $4. Find how many Dinars you would receive if you exchanged $64.

#### Solution:
1. The exchange rate is 1 Dinar = $4. Therefore, for $64:
\[
\text{Dinars received} = \frac{64}{4} = 16
\]

Answer: You would receive 16 Dinars.

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Problem 9:

If you can buy six bulbs of garlic for Rs. 12, then how many can you buy with Rs. 6?

#### Solution:
1. First, find the cost of one bulb of garlic.
\[
\text{Cost of one bulb} = \frac{\text{Total cost}}{\text{Number of bulbs}} = \frac{12}{6} = 2 \text{ Rs.}
\]
2. Now, determine how many bulbs you can buy with Rs. 6.
\[
\text{Number of bulbs} = \frac{\text{Amount available}}{\text{Cost of one bulb}} = \frac{6}{2} = 3
\]

Answer: You can buy 3 bulbs.

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Problem 10:

Deepu bought one seedless watermelon for Rs. 20. How many seedless watermelons can Jill buy if she has Rs. 40?

#### Solution:
1. The cost of one seedless watermelon is Rs. 20.
2. Determine how many watermelons Jill can buy with Rs. 40.
\[
\text{Number of watermelons} = \frac{\text{Amount Jill has}}{\text{Cost of one watermelon}} = \frac{40}{20} = 2
\]

Answer: Jill can buy 2 seedless watermelons.

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Final Answers:

1. 3 bananas
2. 3 inches
3. 3 inches
4. 4 inches
5. 20 Pa'anga
6. $5
7. $5
8. 16 Dinars
9. 3 bulbs
10. 2 seedless watermelons

\boxed{3, 3, 3, 4, 20, 5, 5, 16, 3, 2}