Question

5. The sum of two numbers is 15. The difference between five times the first number and Three times the second number is 19. Find the two numbers.​

Answer 1

x = 8

y = 7

Explanation:

let's assume the first number as x, and the second number as y

Now, according to the question,

x + y = 15

Moving on to the next statement,

five times the first number = 5x

three times the second number = 3y

Thus,

5x - 3y = 19

Now that we have two equations, we can either write 'x' in 'y' terms, or y in 'x' terms.

For example, from the first equation:

x + y = 15

y = 15 - x

Now, let's put this value of y into the second equation, i.e.

5x - 3(15 - x) = 19

5x - 45 +3x = 19

8x = 19 + 45

x = 64/8

x = 8

Now, let's put this value of x into the first equation, i.e.

x + y = 15

8 + y = 15

y = 7

In conclusion, the two numbers, x and y, are 8 and 7 respectively

Answer 2

let the 2 unknown numbers be 'x' and 'y'

given: x+y=15 - equation 1

5x-3y=19 - equation 2

from equation 1 :

x = 15 -y

substitute this in equation 2

5(15-y) -3y = 19

75 - 5y - 3y = 19

75-8y=19

8y=56

y=7(substitute value of y in equation 1)

x+7=15

x=8

hence the two numbers are 8 and 7