Question

Grover, Bert, and Ernie entered a jelly bean-guessing contest in which the winning guess is the closest guess that does not exceed the actual count.
- Grover won the contest; his guess was twice as far from the actual count as Ernie’s guess.
- Bert’s guess of 782 cut Ernie’s error in half.
- The sum of their guesses was 2278.
Find the sum of the digits of the actual number of jelly beans.

i need to see the work

Answer 1

let the number of jelly beans be \( J\)
let Grover, Bert, and Ernie ' guesss be \(G,B,E\) respectively ,

Answer 2

\[2|J-G|=|J-E|\]
\[B=782\]
\[2|J-B|=|J-E|\]
\[G+B+E=2278\]