rrect answer. The cost of a certain number of pens is ₹72. If the cost of each pen is decreased by then 8 more pens can be purchased for the same amount. How many pens can be pucy for the same amount if the cost of each pen is increased by ₹1.50 ?

Define Original Cost: Let x be the original cost of each pen. Then the number of pens that can be bought for ₹72 is 72/x. Calculate New Number of Pens: If the cost of each pen is decreased by ₹1, the new cost per pen is x - 1. Then 8 more pens can be bought, so the new number of pens is 72/(x - 1). Formulate Equation: We have the equation 72/x + 8 = 72/(x - 1). Clear Denominators: Multiply both sides by x(x - 1) to clear the denominators: 72(x - 1) + 8x(x - 1) = 72x. Simplify Equation: Simplify the equation: 72x - 72 + 8x^2 - 8x = 72x. Combine Like Terms: Combine like terms and move all terms to one side: 8x^2 - 8x - 72 = 0. Divide by 8: Divide the entire equation by 8 to simplify: x^2 - x - 9 = 0.

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The cost of a certain number of pens is ₹ $72$ . If the cost of each pen is decreased by ₹ $1$ , then $8$ more pens can be purchased for the same amount. How many pens can be purchased for the same amount if the cost of each pen is increased by ₹ $1$ . $50$ ?

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Grade 6

Evaluate variable expressions: word problems

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Q. The cost of a certain number of pens is ₹

72

. If the cost of each pen is decreased by ₹

1

, then

8

more pens can be purchased for the same amount. How many pens can be purchased for the same amount if the cost of each pen is increased by ₹

1

50

Define Original Cost: Let $x$ be the original cost of each pen. Then the number of pens that can be bought for ₹ $72$ is $72/x$ .
Calculate New Number of Pens: If the cost of each pen is decreased by ₹ $1$ , the new cost per pen is $x - 1$ . Then $8$ more pens can be bought, so the new number of pens is $72/(x - 1)$ .
Formulate Equation: We have the equation $\frac{72}{x} + 8 = \frac{72}{x - 1}$ .
Clear Denominators: Multiply both sides by $x(x - 1)$ to clear the denominators: $72(x - 1) + 8x(x - 1) = 72x$ .
Simplify Equation: Simplify the equation: $72x - 72 + 8x^2 - 8x = 72x$ .
Combine Like Terms: Combine like terms and move all terms to one side: $8x^2 - 8x - 72 = 0$ .
Divide by $8$ : Divide the entire equation by $8$ to simplify: $x^2 - x - 9 = 0$ .