SOLUTION: Hi tutors, please help with the following math problem. Thank you very much. Jack and Mark have 49 beads. Mark and Ben have 37 beads. Jack and Ben have 60 beads. How many beads

Question 473285: Hi tutors, please help with the following math problem. Thank you very much.
Jack and Mark have 49 beads. Mark and Ben have 37 beads. Jack and Ben have 60 beads. How many beads does each of them have and the sum of all?
I tried by adding 49 + 60 then minus 37 and divide 3, which I got 24. After that, i am stuck as I couldn't figure out how many does each boy have. I totaled up the numbers to be 74 but the answer should be 73.
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let J = # of beads Jack has, M = # of beads Mark has, and B = # of beads Ben has

Since "Jack and Mark have 49 beads", we know that . Solve for M to get

Because "Mark and Ben have 37 beads", we know that . Plug in to get . Now solve for B to get --->

Since "Jack and Ben have 60 beads", we see that . Plug in to get , which will simplify to

Now solve for J

So Jack has 36 beads.

So Mark has beads

So Ben has beads

========================================================

Answer:

Jack has 36 beads, Mark has 13 beads, and Ben has 24 beads.

In total, they have 36+13+24 = 73 beads
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Jack and Mark have 49 beads.
Mark and Ben have 37 beads.
Jack and Ben have 60 beads.
--------------------------------
Equations:
0 + j + m = 49
b + 0 + m = 37
b + j + 0 = 60
------------------------
How many beads does each of them have and the sum of all?
----
I used a matrix method to get:
b = 24
j = 36
m = 13
----
# of beads = 24+36+13 = 73
===============================
Cheers,
Stan H.
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