Question

Anne, Ryan, and Joel collect empty cans for recycling. They collect a total of 1925 cans. Anne collects half as many cans as Ryan. Joel collects twice as many cans as Ryan. How many cans does Joel collect?

Answer 1

total cans = 1925,
Anne = 1/2 Ryan
Joel = 2 Ryan                                 [Ryan =R, Anne = A, Joel =J]
therefore R + 1/2R +2R = 1925
taking L.C.M we get,
(2R + 1 +4R)/2 = 1925,
cross multiply we get,
2R +1 +4R = 1925 x 2
2R +1 +4R = 3850
7R = 3850
R = 3850/ 7
R = 550
therefore collection Joel is J =2R
J = 2 x 550
J = 1100.
therefore Joe;l got 1100 cans

Answer 2

Anne = Ryan /2 ,       Hence   Ryan = 2 * Anne

Joel = 2 * Ryan

Joel = 2 * Ryan = 2 * (2 * Anne ) = 4 * Anne

Total cans = Anne + Ryan + Joel  = 1925
         1925       = Anne + 2 * Anne + 4 *anne =  7 * Anne 
      
  Hence Anne = 1925 / 7 = 275

Hence  Ryan = 2 * 275 = 550

Joel = 2 * Ryan = 1100