SOLUTION: If I have 110 coins and I have 24 more half dollar than quarters ,how many of each do I have

Question 1023770: If I have 110 coins and I have 24 more half dollar than quarters ,how many of each do I have
Found 2 solutions by mathmate, addingup:
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

Question:
A club has 60 male members and 50 female members. If the club is to have a contest, where there are all male and all female teams competing, what is the most members a team can have? All teams must be of equal size and everyone must be on a team

Solution:
The rule of the game requires that all teams have the same number of members and everyone must be included. Therefore, the choice of size of teams is dictated by the factors of the size of the group.
For males, size of the group is 60. Its factors are:
1,2,3,4,5,6,10,12,15,20,30,60.
For females, size of the group is 50. Its factors are:
1,2,5,10,25,50.
Since the both the male and female teams must have the same team size, the maximum size acceptable for the game is the largest factor that is common to both groups. For example, 50 is the largest of the female group, but it is not present in the male group, so 50 cannot be the team size.
Can you spot the maximum team size from the above two lists?
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
half dollars: x
quarters: y
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
x+y = 110 (1)
and
x = y+24 (2)
substitute for x in (1):
y+24+y = 110 add y on left and subtract 24 on both sides
2y = 86
y = 43 You have 43 quarters and:
43+24 = 67 half dollars
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