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

Algebra ->  Linear-equations -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!

let the number of marbles Don has be d and the number of marbles Mark has be m
if Don has 3 more than 3 times the number of marbles Mark has, we have
d=3m%2B3...........eq.1

if the total number of marbles is+99, we have
d%2Bm=99............eq.2, substitute d from eq.1
3m%2B3%2Bm=99...........solve for m
4m=99-3
4m=96
m=96%2F4
m=24
go to
d=3m%2B3...........eq.1, substitute m
d=3%2A24%2B3
d=75
answer:
Don has 75 and Mark has 24 marbles.

Answer by greenestamps(13200) About Me  (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.