The sum of two numbers is 2490. If 6.5% of one number is equal to 8.5% of the other, then the numbers are?

The sum of two numbers is 2490. If 6.5% of one number is equal to 8.5% of the other, then the numbers are?

Explanation
  • Let the two numbers be x and y.
    • Given: x + y = 2490 ... (Equation 1)
    • Also, 6.5% of x = 8.5% of y
    • To simplify, convert percentages to decimals: 0.065x = 0.085y
    • Now, divide both sides by 0.065: x = (0.085/0.065)y
    • x = (85/65)y
    • x = (17/13)y ... (Equation 2)
    • Now, substitute Equation 2 into Equation 1:
    • (17/13)y + y = 2490
    • Combine like terms: (30/13)y = 2490
    • Multiply both sides by 13/30: y = 1079
    • Now that we have found y, we can find x:
    • x = 2490 - y (from Equation 1)
    • x = 2490 - 1079
    • x = 1411
    • So, the correct answer is: 1411, 1079