Question

If 5 1/5 = x + 1 3/4 , then x = ?

Answer 1

`\large\boxed{x=3(9)/(20)}`

Explanation:

`5(1)/(5)=x+1(3)/(4)\qquad\text{convert the mixed numbers to the improper fractions}\\\\(5\cdot5+1)/(5)=x+(1\cdot4+3)/(4)\\\\(26)/(5)=x+(7)/(4)\qquad\text{multiply both sides by LCM(5, 4) = 20}\\\\20\!\!\!\!\!\diagup^4\cdot(26)/(5\!\!\!\!\diagup_1)=20x+20\!\!\!\!\!\diagup^5\cdot(7)/(4\!\!\!\!\diagup_1)\\\\(4)(26)=20x+(5)(7)\\\\104=20x+35\qquad\text{subtract 35 from both sides}\\\\69=20x\qquad\text{divide both sides by 20}\\\\(69)/(20)=x\to x=3(9)/(20)`