Word Problems Using Linear Equations

 

❓ Question

Champa went to a sale to purchase some pants and skirts.
When her friends asked how many of each she had bought, she answered:

• “The number of skirts is two less than twice the number of pants purchased.”
• “The number of skirts is four less than four times the number of pants purchased.”

Help her friends find how many pants and skirts Champa bought.

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🖼️ Solution Image

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✍️ Short Concept

Word problems based on pair of linear equations are solved by:

✅ Defining variables
✅ Forming equations from statements
✅ Solving equations simultaneously

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🔷 Step 1 — Define Variables

Let:

$$x = \text{number of pants}$$
$$y = \text{number of skirts}$$

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🔷 Step 2 — Form First Equation

Statement:

“The number of skirts is two less than twice the number of pants.”

Twice the pants:

$$2x$$

Two less than that:

$$y = 2x - 2$$

So first equation is:

$$\boxed{y=2x-2}$$

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🔷 Step 3 — Form Second Equation

Statement:

“The number of skirts is four less than four times the number of pants.”

Four times the pants:

$$4x$$

Four less than that:

$$y = 4x - 4$$

So second equation is:

$$\boxed{y=4x-4}$$

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🔷 Step 4 — Solve Equations

Equating both equations:

$$2x-2 = 4x-4$$

Bring terms together:

$$2 = 2x$$
$$x=1$$

Now substitute in:

$$y=2x-2$$
$$y=2(1)-2$$
$$y=0$$

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🔷 Step 5 — Final Answer

$$\boxed{x=1}$$
$$\boxed{y=0}$$

So, Champa bought:

✅ 1 pair of pants
✅ 0 skirts

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⭐ Important Concept

For word problems:

• “less than” means subtraction
• “more than” means addition
• Convert statements carefully into equations

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📚 Related Topics

• Find Zeroes and Verify Relationship Between Coefficients
• Find Quadratic Polynomial from Sum and Product of Zeroes
• Quadratic Polynomial with Irrational Zeroes Explained