Form the pair of linear equations for the following problems and find their solution by substitution method.

Question

(i) The difference between two numbers is 26 and one number is three times the other. Find them.
(ii) The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.
(iii) The coach of a cricket team buys 7 bats and 6 balls for Rs 3800. Later, she buys 3 bats and 5 balls for Rs 1750. Find the cost of each bat and each ball.

Answer 1

i) Let us assume the larger number is x and smaller number is y. Then we have following equations, as per question:

x = y + 26 and x = 3y

Substituting the value of x from second equation in the first equation, we get;

x = y + 26

Or, 3y = y + 26

Or, 2y = 26

Or, y = 13

Substituting the value of y in second equation, we get;

x = 3y

Or, x = 13 x 3 = 39

Hence, x = 39 and y = 13

ii)  Let us assume the larger angle is x and smaller angle is y. Then we have following equations;

x = y + 18 and x + y = 180o

Substituting the value of x from first equation in second equation, we get;

x + y = 180o

Or, y + 18 + y = 180o

Or, 2y = 180o - 18o = 162o

Or, y = 81o

Substituting the value of y in first equation, we get;

x = y + 18

Or, x = 81o + 18o = 99o

Hence, x = 99o and y = 81o

iii)  Let cost of each bat  =  Rs x

Cost of each ball  = Rs y

Given that coach of a cricket team buys 7 bats and 6 balls for Rs 3800.

So that 7x + 6y = 3800

6y = 3800 – 7x

Divide by 6 we get

y = (3800 – 7x) /6         … (1)

Given that she buys 3 bats and 5 balls for Rs 1750.so that

3x + 5y = 1750

Plug the value of y

3x + 5 ((3800 – 7x) /6) = 1750

Multiply by 6 we get

18 x  + 19000 – 35 x = 10500

-17x =10500 - 19000

-17x = -8500

x = - 8500 / - 17

x =  500

Plug this value in equation first we get

y = ( 3800 – 7 * 500) / 6

y = 300/6

y = 50

Hence cost of each bat = Rs 500 and cost of each balls is Rs 50