Question

Carlo is 3 2/3 years older than his sister if his sister us 18 5/6 years old how old is carlo

Answer 1

`\sf 22(1)/(2)\; years`

Explanation:

`\textsf{First convert all mixed fractions to improper fractions: }\\\\3(2)/(3) = (3 * 3 + 2)/(3)= (11)/(3)\\\\18(5)/(6 ) = (18 * 6 + 5)/(6) = (113)/(6)`

Let Carlo's age be C

Carlo's age = sister's age + 11/3

`\sf == > C = (113)/(6) +\frac {11}{3}\\\\\textsf{Multiply both sides by 6 to eliminate the denominator}\\\\\sf 6C = 6\cdot(113)/(6) + 6\cdot\frac {11}{3}\\\\`

`\sf == > C = (113)/(6) +\frac {11}{3}\\\\\textsf{Multiply both sides by 6 to eliminate the denominator}\\\\\sf 6C = 6\cdot(113)/(6) + 6\cdot\frac {11}{3}\\\\\sf 6C = 113 + 22 = 135\\`

`\textsf {Divide both sides by 6}\\\\\sf C = (135)/(6) \\\\\textsf {Reduce $(135)/(6)$ by dividing numerator and denominator by 3}\\\\== > C = (135 / 3)/(6/3) = (45)/(2)`

`\textsf{So Carlo's age is $(45)/(2)$ or $22(1)/(2)$ years}`