Question 861531
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
:
;
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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