Find the two numbers

Question

The sum of twice a first number and five times a second number is 99. If the second number is subtracted from five times the first number the result is 45. Find the numbers

Answer 1

Let f be the first number and s the second.

2f+5s=99

5f  -s =45

Multiply the first equation by 5 and the second by 2 to get

10f+25s=495

10f   -2s= 90

Subtract to get

27s=405,  or s=15 and from the second equation 5f=60 or f=12