Five times a number and two times another numberadded togethermakes 20.Three times the second numberadded to Two times the first gives 19. What are the numbers?
Answers
The two numbers are 2 and 5
Given :-
Five times a number and two times another number added together makes 20.
Three times the second number added to two times the first gives 19.
To find :-
The two numbers
Solution :-
Let the first number be X
Let the second number be Y
Five times the first number = 5X
Two times the second number = 2Y
According to the given problem
5X+2Y = 20 --------------(1)
Three times the second number = 3Y
Two times the first number = 2X
According to the given problem
2X+3Y = 19 ---------------(2)
On multiplying equation (1) with 2 then
10X+4Y = 40 -------------(3)
On multiplying equation (2) with 5 then
10X+15Y = 95 ------------(4)
On subtracting (3) from (4)
10X+15Y = 95
10X+4Y = 40
(-)
___________
0+11Y = 55
___________
=> 11Y = 55
=> Y = 55/11
=> Y = 5
On substituting the value of Y in (1) then
5X+2(5) = 20
=> 5X +10 = 20
=> 5X = 20-10
=> 5X = 10
=> X = 10/5
=> X = 2
Therefore, X = 2 and Y = 5
The first number = 2
The second number = 5
Answer :-
The required two numbers are 2 and 5 respectively.