Ratios, Algebra

Question

Gold star gets a free pass. For every 2 gold stars there are 18 silver, 16 purple, and 12 green stars handed out. If there are 382 total stars, how many are gold stars?

Answer 1

first we need to calculate ration between gold star and the other three stars

so for every 2 gold star there are 18 silver stars,  

then 18/2 = 9  means for every one gold star there is  9 silver stars

same for 2 gold stars there are 16 purple stars, then 16/2 = 8 means for 1 gold there is 8 purple

also for 2 gold stars there are 12 green stars, then 12/2 = 6 means for 1 gold there is 6 green

 

what if we have x gold stars then we will have

9x silver stars

8x purple stars

6x green stars

so

x + 9x + 8x + 6x = 382-----> 24x = 382   divede both side by 24 we get

x = 328/24 ------>x = 15.9167  which can be almost x ≈ 16 gold stars

 

Best 

Answer 2

So the extended ratio is 2:18:16:12, which means that 48 stars are in a group.

Now 382 is not evenly divisible by 48, therefore a complete set of stars was not distributed and the solution is not possible.