SOLUTION: twice a number exceeds 24 by as much as twice a second number is less than 80.thrice the first number divided by 5 is equal to the second number divided by 4. find the numbers

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Question 669455: twice a number exceeds 24 by as much as twice a second number is less than 80.thrice the first number divided by 5 is equal to the second number divided by 4. find the numbers
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Two numbers, a & a
;
twice a number exceeds 24 by as much as twice a second number is less than 80.
2a - 24 = 80 - 2b
2a + 2b = 80 + 24
2a + 2b = 104
Simplify, divide by 2
a + b = 52
:
thrice the first number divided by 5 is equal to the second number divided by 4.
%283a%29%2F5 = b%2F4
cross multiply
4(3a) = 5b
12a = 5b
12a - 5b = 0
5a + 5b = 260 multiplied the 1st equation by 5
-------------- addition eliminates b, find a
17a = 260
a ~ 15.294, I would have expected integers here, anyway
:
a + b = 52
15.294 + b = 52
b = 52 - 15.294
b = 36.706
:
:
See if that satisfies the 2nd statement, using a calc:
%283%2A15.294%29%2F5 = 36.706%2F4
9.1764 ~ 9.1765, close anyway