# ELIMINATION METHOD WORD PROBLEMS WORKSHEET

## About "Elimination method word problems worksheet"

Elimination method word problems worksheet :

Worksheet on elimination method word problems is much useful to the students who would like to practice solving word problems on linear equations with two variables.

## Elimination method word problems worksheet - Problems

1.  A park charges \$10 for adults and \$5 for kids. How many many adults tickets and kids tickets were sold, if a total of 548 tickets were sold for a total of \$3750 ?

2.  Sum of the cost price of two products is \$50. Sum of the selling price of the same two products is \$52. If one is sold at 20% profit and other one is sold at 20% loss, find the cost price of each product.

## Elimination method word problems worksheet - Problems

Problem 1 :

A park charges \$10 for adults and \$5 for kids. How many many adults tickets and kids tickets were sold, if a total of 548 tickets were sold for a total of \$3750 ?

Solution :

Step 1 :

Let "x" be the no. of adult tickets and "y" be the no. of kids tickets.

According to the question, we have

x + y  =  548 ---------(1)

And also,

10x + 5y  =  3750

Divide both sides by 5.

2x + y  =  750 --------(2)

Step 2 :

Eliminate one of the variables to get the value of the other variable.

In (1) and (2), variable "y" is having the same coefficient. But, the variable "y" is having the same sign in both the equations.

To change the sign of "y" in (1), multiply both sides of (1) by negative sign.

- (x + y)  =  - 548

- x - y  =  - 548 --------(3)

Step 3 :

Now, eliminate the variable "y"in (2) and (3) as given below and find the value of "x".

Step 4 :

Plug x  =  202 in (1) to get the value of y.

(2) --------> 202 + y  =  548

Subtract 202 from both sides.

aaaaaaaaaaaaaaaaaaaa 202 + y  =  548 aaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa- 202         - 202 aaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa------------------- aaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa            y  =  346 aaaaaaaaaaaaaaaaa  aaaaaaaaaaaaaaaaaaa------------------- aaaaaaaaaaaaaaaaa

Hence, the number of adults tickets sold is 202 and the number of kids tickets sold is 346

Problem 2 :

Sum of the cost price of two products is \$50. Sum of the selling price of the same two products is \$52. If one is sold at 20% profit and other one is sold at 20% loss, find the cost price of each product.

Solution :

Step 1 :

Let "x" and "y" be the cost prices of two products.

Then,  x + y  =  50  --------(1)

Step 2 :

Let us assume that "x" is sold at 20% profit

Then, the selling price of "x" is 120% of "x"

Selling price of "x"  =  1.2x

Let us assume that "y" is sold at 20% loss

Then, the selling price of "y" is 80% of "y"

Selling price of "x"  =  0.8y

Given : Selling price of "x"  +  Selling price of "y"  =  52

1.2x + 0.8y  =  52

To avoid decimal, multiply both sides by 10

12x + 8y  =  520

Divide both sides by 4.

3x + 2y  =  130 --------(2)

Step 3 :

Eliminate one of the variables to get the value of the other variable.

In (1) and (2), both the variables "x" and "y" are not having the same coefficient.

One of the variables must have the same coefficient.

So multiply both sides of (1) by 2 to make the coefficients of "y" same in both the equations.

(1) ⋅ 2 -------->  2x + 2y  =  100 ----------(3)

Variable "y" is having the same sign in both (2) and (3).

To change the sign of "y" in (3), multiply both sides of (3) by negative sign.

- (2x + 2y)  =  - 100

- 2x - 2y  =  - 100 --------(4)

Step 4 :

Now, eliminate the variable "y"in (2) and (4) as given below and find the value of "x".

Step 5 :

Plug x  =  30 in (1) to get the value of y.

(2) --------> 30 + y  =  50

Subtract 30 from both sides.

aaaaaaaaaaaaaaaaaaaa    30 + y  =  50 aaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa   - 30         - 30 aaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa------------------- aaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa             y   =  20 aaaaaaaaaaaaaaaaa  aaaaaaaaaaaaaaaaaaa------------------- aaaaaaaaaaaaaaaaa

Hence, the cost prices of two products are \$30 and \$20.

After having gone through the stuff given above, we hope that the students would have understood "Elimination method word problems worksheet".

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

WORD PROBLEMS

HCF and LCM  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