SOLUTION: 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 i

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
:
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

RELATED QUESTIONS
one number is two less than another number. double the first number is equal to triple... (answered by JBarnum)

Two times a first number decreased by a second number is 4. The first number increased by (answered by scott8148)

Find two numbers such that the second number is 2 more than three times the first number, (answered by harpazo)

Find two consecutive whole numbers such that 3/4 of the first number is 5 more than 1/2... (answered by edjones)

Find two consecutive whole numbers such that 4/6 of the first number is 12 more than 1/3... (answered by Stitch)

One number is two more than a second number. Twice the first number is triple the second... (answered by macston)

Twice the first number is increased by the second number is 16. Find the two numbers if... (answered by Alan3354)

consider two numbers the second number is five less than triple the first number. The sum (answered by Alan3354)

Consider two numbers. The second number is five less than triple the first number. The... (answered by LinnW)