Question 738978
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
:
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
;
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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