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Question 738978: Determine two whole numbers such that the first number increased by triple the second number is 24.
If the first number is squared and decreased by five times itself, the result is 13 less than the second number.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Let the two numbers be a & b, write an equation for each statement:
:
Determine two whole numbers such that the first number increased by triple the second number is 24.
a + 3b = 24
3b = (24-a)
divide by 3
b = (8 - a/3); use this form for substitution
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If the first number is squared and decreased by five times itself, the result is 13 less than the second number.
a^2 - 5a = b - 13
Replace b with (8 - a/3)
a^2 - 5a = 8 - a/3 - 13
a^2 - 5a = - a/3 - 5
mult by 3 to get rid of the denominator
3a^2 - 15a = -a - 15
Combine as a quadratic equation on the left
3a^2 - 15a + a + 15 = 0
3a^2 - 14a + 15 = 0
factors to
(3a-5)(a-3) = 0
only integer solution
a = 3
find b
b = 8 - 3/3
b = 7
;
;
See if that works in the given statements
"the first number increased by triple the second number is 24."
3 + 3(7) = 24
"first number is squared and decreased by five times itself, the result is 13 less than the second number."
3^2 - 5(3) = 7 - 13
9 - 15 = -6
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