SOLUTION: 24 boxes are carried by 24 people. Adults can carry 3 boxes Teenages can carry 2 boxes and 3 children can carry 1 box. How do I figure hown many of which people carried how many

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Question 290306: 24 boxes are carried by 24 people. Adults can carry 3 boxes Teenages can carry 2 boxes and 3 children can carry 1 box. How do I figure hown many of which people carried how many boxes. Some thing like 3 adults 2 teenagers and 6 children???
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
24 boxes are carried by 24 people.
Adults can carry 3 boxes Teenagers can carry 2 boxes and 3 children can carry 1 box.
How do I figure how many of which people carried how many boxes.
:
Total people equation:
a + t + c = 24
:
Let each child carry 1/3 of box
3a + 2t + 1%2F3c = 24
Multiply by 3 and use elimination with the first equation:
9a + 6t + c = 72
a + t + c = 24
-------------------subtraction eliminates c
8a + 5t = 48
8a = 48 - 5t
Divide eq by 8:
a = 6 - 5%2F8t
We must have an integer solution; t has to be a multiple of 8, but not 16
t=8
a = 6 - 5
a = 1
:
1 adult, 8 teenagers
:
Find the number of children
1 + 8 + c = 24
c = 24 - 9
c = 15 children
:
Check by finding the number of boxes
1(3) + 8(2) + 1%2F315 = 24
3 + 16 + 5 = 24 boxes
;
1 adult, 8 teenagers, 15 children