Question

linear equation in two variable word problems

Answer 1

1. The sum of two number is 14 and their difference is 2. Find the numbers.

Solution:

Let the two numbers be x and y.
x + y = 14 ………. (i)
x - y = 2 ………. (ii)
Adding equation (i) and (ii), we get 2x = 16
or, 2x/2 = 16/2 or, x = 16/2
or, x = 8

Substituting the value x in equation (i), we get
8 + y = 14
or, 8 – 8 + y = 14 - 8
or, y = 14 - 8
or, y = 6

Therefore, x = 8 and y = 6
Hence, the two numbers are 6 and 8.



2. In a two digit number. The units digit is thrice the tens digit. If 36 is added to the number, the digits interchange their place. Find the number.

Solution:

Let the digit in the units place is x
And the digit in the tens place be y.
Then x = 3y and the number = 10y + x
The number obtained by reversing the digits is 10x + y.

If 36 is added to the number, digits interchange their places,
Therefore, we have 10y + x + 36 = 10x + y
or, 10y – y + x + 36 = 10x + y - y
or, 9y + x – 10x + 36 = 10x - 10x
or, 9y - 9x + 36 = 0 or, 9x - 9y = 36
or, 9(x - y) = 36
or, 9(x - y)/9 = 36/9
or, x - y = 4 ………. (i)

Substituting the value of x = 3y in equation (i), we get
3y - y = 4
or, 2y = 4
or, y = 4/2
or, y = 2

Substituting the value of y = 2 in equation (i),we get
x - 2 = 4
or, x = 4 + 2
or, x = 6
Therefore, the number becomes 26.


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3. If 2 is added to the numerator and denominator it becomes 9/10 and if 3 is subtracted from the numerator and denominator it become 4/5. Find the fractions.


Solution:

Let the fraction be x/y.

If 2 is added to the numerator and denominator fraction becomes 9/10 so, we have

(x + 2)/(y + 2) = 9/10

or, 10(x + 2) = 9(y + 2)

or, 10x + 20 = 9y + 18

or, 10x – 9y + 20 = 9y – 9y + 18

or, 10x – 9x + 20 – 20 = 18 – 20

or, 10x – 9y = -2 ………. (i)

If 3 is subtracted from numerator and denominator the fraction becomes 4/5 so, we have

(x – 3)/(y – 3) = 4/5

or, 5(x – 3) = 4(y – 3)

or, 5x – 15 = 4y – 12

or, 5x – 4y – 15 = 4y – 4y – 12

or, 5x – 4y – 15 + 15 = – 12 + 15

or, 5x – 4y = 3 ………. (ii)

So, we have 10x – 9y = – 2 ………. (iii)

and 5x – 4y = 3 ………. (iv)

Multiplying both sided of equation (iv) by 2, we get

10x – 8y = 6 ………. (v)

Now, solving equation (iii) and (v) , we get

10x – 9y = -2

10x – 8y = 6
- y = - 8

y = 8


Substituting the value of y in equation (iv)

5x – 4 × (8) = 3

5x – 32 = 3

5x – 32 + 32 = 3 + 32

5x = 35

x = 35/5

x = 7

Therefore, fraction becomes 7/8.


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