Worksheet 3
Pair of linear equations
1. The sum of two numbers is 50 and their difference is 22. Find the numbers.
2. One number is three times the other number. The differ en ce between the two
numbers is 12. Find the two numbers.
3. The sum of two numbers is 9. The difference in their squares is also 9. Find
the number.
4. The differ en ce between the two numbers is 7. Two times the smaller number
added to the larger number gives 22. Find the two numbers.
5. 3 tab les and 2 chairs cost Rs. 1900 and 2 tables and 4 chairs cost Rs. 1800.
Find the cost of tab le and a ch air
6. A lady has only Rs. 1 and Rs 2 co in in her purse. If in all she has 50 coins
to taling Rs. 70, Find the number of coins of each type.
7. I am three times old as my son. After five years, I will be 212 times as old as
my son. Find my present age and the present age of my son.
3. Ten years ago, mother was 12 times as old as her daughter and ten years
hence she will be twice as old as her daughter will be. Find the present ages.
Answers
Answer:
1.x+y=50
x-y=22
Adding these both,
x+y+x-y=50+22
2x=72
x=36
y=50-36=14
2.Let the 2 no.s be x and y
x=3y
x-y=12
Therefore,3y-y=12
2y=12
y=6
Therefore x=18
3.x+y=9
x^2-y^2=9
Therefore,x+y=x^2-y^2
now,x^2-y^2=(x+y)(x-y)
Therefore,x+y=(x+y)(x-y)
1=x-y
now,adding x-y=1 and x+y=9,
x-y+x+y=9+1
2x=10
x=5
4.x-y=7
2x+y=22
Now,x=7+y (from first equation)
So,substituting values in 2nd equation,
2(7+y)+y=22
14+2y+y=22
3y=8
y=8/3
So,x,
x-8/3=7
x=29/3
5.3x+2y=1900
2x+4y=1800. (tables-x and chairs-y)
Multiplying equation 1 by 2,
And subtracting equation 2 from 1,
6x+4y-2x-4y=1900-1800
4x=1000
x=250
Therefore,table=250
Chair=575
6.Let the 1rs coins be x and 2rs coins be y,
So,x+2y=70
x+y=50
Subtracting 2 from 1,
x+2y-x-y=70-50
y=20
So,no of 2rs coins=20
no. Of 1rs coins=30
7.Are you sure it's 212 times?
8.present age=x and y
10yrs ago
x-10=(y-10)12
10yrs later,
x+10=(y+10)2
Subtracting 2 from 1,
(x-10)-(x+10)=(12y-120)-(2y+20)
-20=10y-140
120=10y
12=y
Daughter's present age-12
Mother's present age-34
Hope I helped!