Question 861531: Tomas, Rick and Larry are three brothers. Tomas, who is the oldest is not yet 40. The sum of the ages of the brothers is 73 and the product of Tomas and Larry's age is 750. Furthermore, the difference between Tomas' age and Ricks age is 7 years greater than the difference between Tomas and Larry's age. How old is Rick?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Tomas, Rick and Larry are three brothers.
Tomas, who is the oldest is not yet 40.
t < 40
The sum of the ages of the brothers is 73
t + r + L = 73
and the product of Tomas and Larry's age is 750.
t * L = 750
Furthermore, the difference between Tomas' age and Ricks age is 7 years greater than the difference between Tomas and Larry's age.
t - r = t - L + 7
subtract t from both sides
-r = -L + 7
rearrange to
-r + L = 7
Add to the 1st equation
t + r + L = 73
0 - r + L = 7
----------------Adding eliminates r
t + 2L = 80
t = -2L + 80
In the equation t * L = 750, replace t
(-2L + 80)*L = 750
-2L^2 + 80L - 750 = 0
Simplify, divide -2
L^2 - 40L + 375 = 0
Factors to
(L-25)(L-15) = 0
L = 25, Or L = 15
t > 40 therefore
L = 25 yrs is Larry's age
then
t = -2(25) + 80
t = 30 yrs is Tomas
and
30 + r + 25 = 73
r = 73 - 55
r = 18 yrs is Rick
:
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Check this in the statement:
"the difference between Tomas' age and Ricks age is 7 years greater than the difference between Tomas and Larry's age."
30 - 18 = 30 - 25 + 7
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