# WORD PROBLEMS WITH QUADRATIC EQUATIONS EXAMPLES

Example 1 :

The diagonal of a rectangular field is 60 meters more than the shorter side. If the longer side is 30 meters more than the shorter side, find the sides of the field.

Solution :

Let x be the length of shorter side of the rectangle

Then,

length of diagonal  =  x + 60

length of longer side  =  x + 30 (x + 60)2   =  x2 + (x + 30)2

x2 + 602 + 2(x)(60)  =  x2 + x2 + 2(x)(30) + 302

x2 + 3600 + 120x  =  2x2 + 60x + 900

2x2 - x+ 60x - 120x + 900 - 3600  =  0

x2 - 60x - 2700  =  0

x2 - 90x + 30x - 2700  =  0

x(x - 90) + 30(x - 90)  =  0

(x + 30)(x - 90)  =  0

x + 30  =  0  or  x - 90  =  0

x  =  -30  or  x  =  90

Because x represents breadth of the rectangle, it can not take a negative value.

Then,

x  =  90

So,

breadth of rectangle  =  90 m

length of rectangle  =  90 + 30  =  120 m

Example 2 :

The difference of squares of two positive numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.

Solution :

Let 'x' be the larger number

let 'y' be the smaller number

The square of the smaller number is 8 times the larger number.

y2  =  8x -----(1)

The difference of squares of two numbers is 180.

x2 - y2  =  180

x2 - 8x  =  180

x2 - 8x - 180  =  0

x2 - 18x + 10x - 180  =  0

x(x - 18) + 10(x - 18)  =  0

(x - 18)(x + 10)  =  0

x - 18  =  0  or  x + 10  =  0

x  =  18  or  x  =  -10

Because the numbers are positive, 'x' can not take a negative value.

Then,

x  =  18

Substitute x  =  18 in (1).

y2  =  8(18)

y  =  √[8(18)]

y  =  √(2 · · 2 · 3 · 3 · 2)

y  =  2 · 2 · 3

y  =  12

So, the larger number is 18 and the smaller number is 12.

Example 2 :

A train travels 360 km at a uniform speed. If the speed had been 5 km/h more,it would have taken 1 hour less for the same journey. Find the speed of the train.

Solution :

Let x be the speed of the train

If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey

Time  =  distance/speed

Distance to be covered  =  360 km

T1  =  360/x

T2  =  360/(x + 5)

T1 - T2  =  1 hour

[360/x] -  [360/(x + 5)]  =  1

360[1/x - 1/(x + 5)]  =  1

360[(x + 5 - x) / x(x + 5)]  =  1

360[5 / (x2 + 5x)]  =  1

1800 / (x2 + 5x)  =  1

1800  =  (x2 + 5x)

x2 + 5x - 1800  =  0

x2 - 40x + 45x - 1800  =  0

x(x - 40) + 45(x - 40)  =  0

(x - 40)(x + 45)  =  0

x - 40  =  0     x + 45  =  0

x  =  40   and x  =  -45

Because x represents the speed of the train, it can not take a negative value.

Then,

x  =  40

Therefore speed of the train is 40 km/hr. Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

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

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

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

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6 