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The ratio of Aiden to Daniel's savings was 4:54:5 at first. After Aiden saved another $138\$138 and Daniel saved another $39\$39, Aiden had twice of Daniel's amount. How much did Aiden have in the end?

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Full solution

Q. The ratio of Aiden to Daniel's savings was 4:54:5 at first. After Aiden saved another $138\$138 and Daniel saved another $39\$39, Aiden had twice of Daniel's amount. How much did Aiden have in the end?
  1. Initial Savings Setup: Let's call Aiden's initial savings $4x\$4x and Daniel's initial savings $5x\$5x, where xx is a common factor.
  2. Updated Savings Calculation: After saving more, Aiden has $4x+$138\$4x + \$138 and Daniel has $5x+$39\$5x + \$39.
  3. Equation Setup: Now, Aiden has twice the amount of Daniel, so we set up the equation: $4x+$138=2($5x+$39)\$4x + \$138 = 2(\$5x + \$39).
  4. Equation Solving: Solving the equation: 4x+138=10x+784x + 138 = 10x + 78.
  5. Subtraction Step: Subtract 4x4x from both sides to get 138=6x+78138 = 6x + 78.
  6. Final Division: Subtract $78\$78 from both sides to get $60=$6x\$60 = \$6x.
  7. Finding x Value: Divide both sides by $6\$6 to find x, so x=$10x = \$10.
  8. Aiden's Final Amount: Now we find Aiden's final amount: $4x+$138=$4(10)+$138=$40+$138\$4x + \$138 = \$4(10) + \$138 = \$40 + \$138.
  9. Aiden's Final Amount: Now we find Aiden's final amount: 4x+138=4(10)+138=40+1384x + 138 = 4(10) + 138 = 40 + 138.Aiden's final amount is 40+138=17840 + 138 = 178.

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