**Solving Word Problems Involving Quadratic Equations :**

Here we are going to see some example problems on solving word problems involving quadratic equations.

**Step 1 :**

Convert the information given into to a quadratic equation.

**Step 2 :**

Solve the quadratic equation obtained using one of the methods given below.

1. Factoring

2. Quadratic formula

3. Completing square method

**Step 3 :**

Relate the solution obtained from one of the methods to the statement asked in the question.

**Question 1 :**

If the difference between a number and its reciprocal is 24/5, find the number.

**Solution :**

**Let "x" be the required number "1/x" be its reciprocal.**

**x - (1/x) = 24/5**

**(x ^{2} - 1)/x = 24/5**

**5****(x ^{2} - 1) = 24x**

**5****x ^{2} - 5 = 24x**

**5****x ^{2} - 24x - 5 = 0**

**5****x ^{2} - 25x + 1x - 5 = 0**

**5x(x - 5) + 1(x - 5) = 0**

**(5x - 1) (x - 5) = 0**

**5x - 1 = 0 or x - 5 = 0**

**x = 1/5 or x = 5**

Hence the required numbers are 5 and 1/5.

**Question 2 :**

A garden measuring 12m by 16m is to have a pedestrian pathway that is ‘w’ meters wide installed all the way around so that it increases the total area to 285 m^{2}. What is the width of the pathway?

**Solution :**

From the picture given above, length of the garden including pathway is 12 + 2w and width is 16 + 2w.

length ⋅ width = 285 m^{2}

(12 + 2w) ⋅ (16 + 2w) = 285

192 + 24w + 32w + 4w^{2} = 285

4w^{2 }+ 56w + 192 - 285 = 0

4w^{2 }+ 56w - 93 = 0

a = 4, b = 56 , c = -93

x = [-b ± √b^{2} - 4ac]/2a

x = [-56 ± √(56)^{2} - 4(4)(-93)]/2(4)

x = [-56 ± √(3136 + 1488)]/8

x = [-56 ± 68]/8

x = (-56 + 68) /8 and x = (-56 - 68)/8

x = 12/8

x = 1.5 m

Hence the required width is 1.5 m.

**Question 3 :**

A bus covers a distance of 90 km at a uniform speed. Had the speed been 15 km/hour more it would have taken 30 minutes less for the journey. Find the original speed of the bus.

**Solution :**

Distance covered = 90 km

Let "x" be the original speed of the bus

Increased speed = x + 15

Time = Distance / Speed

Time taken by the bus when it travels in original speed = 90/x

Time taken by the bus when it travels in increased speed = 90/(x + 15)

[90/x] - [90/(x + 15)] = 1/2

90[(x + 15 - x)/x(x + 15)] = 1/2

15/x^{2} + 15x = 1/180

2700 = x^{2} + 15x

x^{2} + 15x - 2700 = 0

x^{2} + 60x - 45x - 2700 = 0

x(x + 60) - 45(x + 60) = 0

(x - 45) (x + 60) = 0

x = 45

Hence the original speed of the bus is 45 km per hour.

After having gone through the stuff given above, we hope that the students would have understood, how to solve word problems involving quadratic equations.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**