How many pebbles did Marc collect?

Question

Abby collected 3 times as many pebbles as James. Marc collected 21 fewer pebbles than Abby. Altogether they collected 294 pebbles. How many pebbles did Mark collect?

Answer 1

For these sorts of questions, I prefer using no algebra. First, let me turn Mark into Abby, by giving him 21 more pebbles: now, we have 2 Abbies and James, collecting a total of 294 + 21 = 300 + 15 = 315 pebbles. Next, each Abby can be turned into 3 Jameses, so that it is now 7 Jameses who collected 315 pebbles. Then, James collected 315 / 7 = 45. (I think of 315 as 280 + 35, which makes dividing it by 7 in my mind easy). Therefore, Abby collected 3 * 45 = 120 + 15 = 135, and Mark got 135 - 21 = 114.

Answer 2

Abby = 3James James = Abby/3  Marc=abby-21  Abby + Marc + James = 294  

 

Abby + (Abby-21) + (Abby/3) = 294

 

2Abby + (Abby/3) = 315

 

6Abby/3 + abby/3 = 315

 

7Abby/3 = 315

7Abby = 945

 

Abby = 135

 

Marc = 114

 

James = 45