A sum of money is to be divided among Ann, Bob and Chloe. First, Ann receives $4 plus one-half of what remains. Next, Bob receives $4 plus one-third of what remains. Finally, Chloe receives the remaining $32. How much money did Bob receive? A) 20 B) 22 C) 24 D) 26 E) 52

A) 4 + (x-4)/2 B) 4 + 1/3 [(X-12)/2] C) 2/3 [(X-12)/2] = 32 ; (x-12) = 3 x 32 SO 4 + 1/3 [(X-12)/2] = 4+ 1/3 ( 3x32/2) = 20

So they had 108 dollars total A ) 4 + 104/2 = 4+ 52 ( 52 remained ) B ) 4 + 1/3 ( 48 ) = 20 ( 32 remained ) C) 32

Nice work, Logitech My solution is below. Note that we don’t need to consider Ann’s portion in the solution. We can just let K be the money remaining after Ann has received her portion and go from there. Our equation will use the fact that, once we remove Bob’s portion, we have $32 for Chloe. So, we get K – Bob’s $ = 32 The equation is K-4 – (K-4)/3 = 32 Solve for K (K=52) and then determine Bob’s portion ($20). The answer is, indeed, A

that was great Brent. It shaved off half the steps.

Bob took $4 + 1/3 of leftover.. that implies 2/3rds is left for Chloe.. if 2/3 of leftover = $32 1/3 of leftover = $16 $16+$4 = $20.

The equation is K-4 – (K-4)/3 = 32 ? K - 4 - k + 4 = 96?

kamu wrote:Bob took $4 + 1/3 of leftover.. that implies 2/3rds is left for Chloe.. if 2/3 of leftover = $32 1/3 of leftover = $16 $16+$4 = $20. that's BRILLIANT!

Brent Hanneson wrote:Nice work, Logitech My solution is below. Note that we donï¿½t need to consider Annï¿½s portion in the solution. We can just let K be the money remaining after Ann has received her portion and go from there. Our equation will use the fact that, once we remove Bobï¿½s portion, we have $32 for Chloe. So, we get K ï¿½ Bobï¿½s $ = 32 The equation is K-4 ï¿½ (K-4)/3 = 32 Solve for K (K=52) and then determine Bobï¿½s portion ($20). The answer is, indeed, A One of the rules that I had read was that normally there is no 'useless' information that is provided, so in case you can solve a sum without using all the inforamation then you must be wrong. How does one know that all the complicated information in this sum is not to be used??