SOLVING WORD PROBLEMS USING CROSS MULTIPLICATION METHOD

Solving Word Problems Using Cross Multiplication Method :

In this section, we will learn, how to solve word problems using cross multiplication method.

Cross Multiplication Method Examples with Answers

Example 1 :

A part of monthly hostel charges is fixed and remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay Rs.1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs.1180 as hostel charges. Find the fixed charge and the cost of food per day.

Solution :

Let “x” be the fixed charge

Let “y” be the charge of food per day

x + 20y  =  1000

x + 26y  =  1180

x + 20y – 1000  =  0  ------(1)

x + 26y – 1180  =  0   ------(2)  x/(-23600 + 26000)  =  y/(-1000 + 1180)  =  1/(26 - 20)

x/2400  =  y/180  =  1/6

x/2400  =  1/6           y/180  =  1/6

x  =  2400/6                y  =  180/6

x  =  400                      y  =  30

Therefore the fixed charge  =  Rs.400

Charge of food per day  =  Rs.30

Example 2 :

A fraction becomes 1/3 when 1 is subtracted from the numerator it becomes 1/4 when 8 is added to its denominator. Find the fraction.

Solution :

Let “x/y” be the required fraction

(x – 1)/ y  =  1/3

3(x – 1)  =  1 y

3 x – 3  =  y

3 x – y – 3  =  0 ----------(1)

x/(y + 8)  =  1/4

4 x  =  1( y + 8)

4 x  =  y + 8

4 x – y – 8  =  0  ----------(2)  x/(8 – 3)  =  y/(-12 + 24)  =  1/(-3 + 4)

x/5  =  y/12  =  1/1

x/5  =  1         y/12  =  1

x  =  5               y  =  12

So, the required fraction is 5/12

Example 3 :

Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?

Solution :

Let “x” be the number of questions answered correctly

Let “y” be the number of questions answered incorrectly

3x  – 1y  =  40

4x – 2y  =  50

3x – 1y – 40  =  0  ---------(1)

4x – 2y – 50  =  0   ---------(2) x/(50 – 80)  =  y/(-160 + 150)  =  1/(-6 + 4)

x/(-30)  =  y/10  =  1/(-2)

x  =  -30/(-2)         y  =  10/(-2)

x  =  15                  y  =  5

So, the number of questions answered correctly = 15

Number of questions answered incorrectly = 5 After having gone through the stuff and examples,  we hope that the students would have understood, solving word problems using cross multiplication method.

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 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

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 