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How to solve Quadratic word problems




Quadratic word problems

We have seen how to solve the quadratic equations ,now lets take a look at the real world problem and how we can apply the quadratic equation formula to solve them

Let start with an example
"In a class test, the sum of Rekha marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects."

How to approach this Problem
a) First we need to carefully read the problem and understand the situation. Here we need to find marks. Let us marks in Maths as $x$,
Then as per problem
Marks in English would be = $30 -x$

b) Now If she got 2 marks less,then Maths marks would = $(x-2)$
c) If she got 3 marks less in English,then English marks would = $(30 -x-3)= (27-x)$
d) As per problem, the product is equal to 210 so
$(x-2)(27-x) =120$
$-x^2 + 25x + 54 = 210$
or
$x^2 - 25x + 156 = 0$
So this is quadratic equation , we can solve by any methods, Solving by factoring method
$x^2 - 90x + 30x - 2700 = 0$
or x =12 or 13

So Rekha maths marks is 12, the English marks are 18
and Rekha maths marks is 13, the English marks are 17
Similarly we can solve the other quadratic word problems



Tips for quadratic word problems

  1. Carefully read down the full problem and understand the situation. Note down what all need to be find out . Choose one of them as the variable x
  2. Now looks for the condition, operations given in the word problem and find all the other quantities in term of variable x
  3. Here are some of the operation which you can find in word problem and their mathematical meaning
    Addition: added to, combined, increased by, more than, sum, total, from now
    Subtraction: decreased by, difference of, less than,ago
    Multiplication: increased by a factor of, multiplied by, times,product
    Division: out of, per, ratio of
    Equals: are, gives, is, will be
  4. Now go for the condition given in the problem and formula the mathematical equation
  5. You can rearrange them to form of quadratic equation
  6. Now you can solve the equation using factorization, square method or quadratic formula
  7. Both the roots may not satisfy the word problem, so always verify it with the problem.Many times negative roots are not the solution of word problem
Check out Quadratic equation Quiz
Check out Quadratic Formula Calculator
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Practice Question

Question 1 What is $1 - \sqrt {3}$ ?
A) Non terminating repeating
B) Non terminating non repeating
C) Terminating
D) None of the above
Question 2 The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is?
A) 19.4 cm3
B) 12 cm3
C) 78.6 cm3
D) 58.2 cm3
Question 3 The sum of the first three terms of an AP is 33. If the product of the first and the third term exceeds the second term by 29, the AP is ?
A) 2 ,21,11
B) 1,10,19
C) -1 ,8,17
D) 2 ,11,20