Question 257661
Let x = the larger number
Let y = the smaller
:
Write an equation for each statement:
:
If larger of two numbers is divided by the smaller, the quotient & remainder are 2 each.
x - 2y = 2
x = 2y + 2 (x equals the quotient(2) times the divisor(y) plus the remainder)
:
if 5 times the smaller number is divided by the larger number, the quotient & remainder are still 2 each.
5y - 2x = 2
5y = 2x + 2
Replace x with (2y+2) in the above equation
5y = 2(2y+2) + 2
5y = 4y + 4 + 2
5y - 4y = 6
y = 6
then
x = 2(6) 2
x = 14
:
14 and 6 are the two numbers
:
:
Check solution in the equation 5y - 2x = 2
5(6) - 2(14) = 2
30 - 28 = 2