Question 805860: one number is 6 more than 3 times another. Their product is 6 more than 3 times their sum. Find the numbers. Answer in the form of paired points with the lowest of the two integers first.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Two numbers, a & b
Write an equation for each statement:
:
"one number is 6 more than 3 times another."
a = 3b + 6
:
" Their product is 6 more than 3 times their sum."
ab = 3(a+b) + 6
ab = 3a + 3b + 6
Replace a with (3b+6)
b(3b+6) = 3(3b+6) + 3b + 6
3b^2 + 6b = 9b + 18 + 3b + 6
3b^2 + 6b = 12b + 24
Combine like terms on the left, to forma quadratic equation
3b^2 + 6b - 12b - 24 = 0
3b^2 - 6b - 24 = 0
simplify divide by 3
b^2 - 2b - 8 = 0
factors to
(b-4)(b+2) = 0
the positive solution is what we want here
b = 4
Find a
a = 3(4) + 6
a = 18
:
Find the numbers. Answer in the form of paired points with the lowest of the two integers first.
4, 18; are the numbers
:
:
Check this out using,"ab = 3(a+b) + 6"
18*4 = 3(18+4) + 6
72 = 3(22) + 6; confirms our solutions
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