Mathematics · Quadratic Equations · NCERT Examples

Example 1

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Mathematics · Chapter 4 · NCERT Examples

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NCERT Example

Example 1

forming quadratic equations · word problems

Represent the following situations mathematically.

John and Jivanti together have 45 marbles. After each loses 5 marbles, the product of the numbers left is 124.
A cottage industry makes x toys in a day. The cost per toy is ₹(55 − x), and the total cost is ₹750.

Solution

Let John initially have x marbles; Jivanti has 45 − x. After the losses:
$(x-5)(40-x)=124$
$-x^2+45x-324=0\Rightarrow x^2-45x+324=0$
Let x be the number of toys. Then:
$x(55-x)=750$
$x^2-55x+750=0$

Final answer

The required equations are x² − 45x + 324 = 0 and x² − 55x + 750 = 0.