SOLUTION: Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 3 more than 3 times the number of marbles Mark has, how many does each boy have to s

Question 1196652: Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 3 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 99?
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

let the number of marbles Don has be and the number of marbles Mark has be
if Don has more than times the number of marbles Mark has, we have
...........eq.1

if the total number of marbles is, we have
............eq.2, substitute from eq.1
...........solve for

go to
...........eq.1, substitute

answer:
Don has and Mark has marbles.

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Presumably the intent of the problem was that you solve it using formal algebra; the other tutor showed one typical formal solution.

You can get good problem-solving practice by solving the problem informally, using logical reasoning and simple mental arithmetic.

(1) Set aside the 3 "extra" marbles that Don has. That leaves 96 other marbles, with Don having 3 times as many as Mark.
(2) That means Mark has 1/4 of those remaining 96 marbles (24), and Don has 3/4 of them (3*24 = 72).
(3) Now give Don's "extra" 3 marbles back to him, giving him 72+3 = 75.

ANSWER: Mark has 24 marbles; Don has 75.

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