# WORD PROBLEMS ON SIMPLE EQUATIONS Problem 1 :

18 is taken away from 8 times of a number is 30. Find the number.

Solution :

Let "x" be the number.

Given : 18 is taken away from 8 times of the number is 30

Then, we have

8x - 18  =  30

8x  =  48

Divide both sides by 8.

x  =  6

Hence, the number is 6.

Problem 2 :

The denominator of a fraction exceeds the numerator by 5. If 3 be added to both, the fraction becomes 3/4. Find the fraction.

Solution :

Let "x" be the numerator.

"The denominator of the fraction exceeds the numerator"

From the above information,

Fraction  =  x / (x + 5) ----------(1)

"If 3 be added to both, the fraction becomes 3 / 4"

From the above information, we have

(x+3) / (x + 5 + 3)  =  3 / 4

Simplify.

(x + 3) / (x + 8)  =  3/4

4(x + 3)  =  3(x + 8)

4x + 12  =  3x + 24

x  =  12

Plug x  = 12 in (1)

Fraction  =  12 / (12 + 5)

Fraction  =  12 / 17

Hence, the required fraction is 12 / 17.

Problem 3 :

If thrice of A's age 6 years ago be subtracted from twice his present age, the result would be equal to his present age. Find A's present age.

Solution :

Let "x" be A's present age.

A's age 6 years ago  =  x - 6

Thrice of A's age 6 years ago  =  3(x-6)

Twice his present age  =  2x

Given : Thrice of A's age 6 years ago be subtracted from twice his present age, the result would be equal to his present age.

So, we have

2x - 3(x - 6)  =  x

Simplify.

2x - 3x + 18  =  x

- x + 18  =  x

18  =  2x

Divide both sides by 2.

9  =  x

Hence, A's present age is 9 years.

Problem 4 :

A number consists of two digits. The digit in the tens place is twice the digit in the units place. If 18 be subtracted from the number, the digits are reversed. Find the number.

Solution :

Let "x" be the digit in units place.

Then, the digit in the tens place  =  2x

So, the number is (2x)x.

Given : If 18 be subtracted from the number, the digits are reversed.

So, we have

(2x)x - 18  =  x(2x)

(2x)x - 18  =  x(2x)

10 ⋅ (2x) + 1 ⋅ x - 18  =  10 ⋅ x + 1 ⋅ (2x)

Simplify.

20x + x - 18  =  10x + 2x

21x - 18  =  12x

21x - 18  =  12x

9x  =  18

Divide both sides by 9.

x  =  2

The digit at the units place is 2.

Then, the digit at the tens place is

=  2 ⋅ 2

=  4

Hence the required number is 42.

Problem 5 :

For a certain commodity, the demand equation giving demand "d" in kg, for a price "p" in dollars per kg. is d = 100(10 - p). The supply equation giving the supply "s" in kg. for a price "p" in dollars  per kg is s = 75(p - 3). Find the equilibrium price.

Solution :

The equilibrium price is the market price where the quantity of goods demanded is equal to the quantity of goods supplied.

So, we have

d  =  s

100(10 - p)  =  75(p - 3)

Simplify.

1000 - 100p  =  75p - 225

1225  =  175p

Divide both sides by 175.

7  =  p

Hence, the equilibrium price is \$7.

Problem 6 :

The fourth part of a number exceeds the sixth part by 4. Find the number.

Solution :

Let "x" be the required number.

Fourth part of the number  =  x/4

Sixth part of the number  =  x/6

Given : The fourth part of a number exceeds the sixth part by 4.

x/4 - x/6  =  4

L.C.M of (4, 6) is 12.

(3x/12) - (2x/12)  =  4

Simplify.

(3x - 2x) / 12  =  4

x / 12  =  4

Multiply both sides by 12.

x  =  48

Hence, the required number is 48.

Problem 7 :

The width of the rectangle is 2/3 of its length. If the perimeter of the rectangle is 80 cm. Find its area.

Solution :

Let "x" be the length of the rectangle.

Then, width of the rectangle  is 2x / 3

Given : Perimeter is 80cm.

Perimeter  =  80 cm

⋅ (l + w)  =  80

Divide both sides by 2.

l + w  =  40

Plug l  =  x and w  =  2x / 3.

x + 2x / 3  =  40

Simplify.

(3x + 2x) / 3  =  40

5x / 3  =  40

Multiply both sides by 3/5.

x  =  24

The length is 24 cm.

Then, the width is

=  2x / 3

=  (2 ⋅ 24) / 3

=  16 cm

Formula to find the area of a rectangle is

=  l ⋅ w

Plug l  =  24 and w  =  16.

=  24 ⋅ 16

=  384

Hence, area of the rectangle is 384 square cm.

Problem 8 :

In a triangle, the second angle is 5° more than the first angle. And the third angle is three times of the first angle. Find the three angles of the triangle.

Solution :

Let x° be the first angle.

Then, we have

the second angle  =  x° + 5°

third angle  =  3 ⋅ x°

We know that the sum of three angle in any triangle is 180°.

x° + (x° + 5°) + (3 ⋅ x°)  =  180°

x + x + 5 + 3x  =  180

Simplify.

5x + 5  =  180

Subtract 5 from both sides.

5x  =  175

Divide both sides by 5.

x  =  35

The first angle is 35°.

The second angle is

=  35° + 5°

=  40°

The third angle is

=  3 ⋅ 3

=  105°

Hence, the three angles of the triangle are 35°, 40° and 105°. Apart from the stuff given in this section if you need any other stuff in math, please use our google custom search here.

If you have any feedback about our math content, please mail us :

v4formath@gmail.com

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

Featured Categories

Math Word Problems

SAT Math Worksheet

P-SAT Preparation

Math Calculators

Quantitative Aptitude

Transformations

Algebraic Identities

Trig. Identities

SOHCAHTOA

Multiplication Tricks

PEMDAS Rule

Types of Angles

Aptitude Test 