SOLUTION: The sum of 3 times Gary's age and 5 times Tom's age is 150. Tom is 9 years less than twice as old as Gary is. How old is Tom?

Question 27685: The sum of 3 times Gary's age and 5 times Tom's age is 150. Tom is 9 years less than twice as old as Gary is. How old is Tom?

Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
The sum of 3 times Gary's age and 5 times Tom's age is 150. Tom is 9 years less than twice as old as Gary is. How old is Tom?
Let Gary's age be G years
and Tom's age be T years.
Given the sum of 3times Gary's age and 5 times Tom's age is 150
The sum of 3G and 5T is 150
That is 3G + 5T = 150 ----(1)
Tom is 9 years less than twice as old as Gary is.
T is 9 less than 2G
That is 2G is greater than T by 9
That is 2G - T = 9 ----(2)
(1) and (2) art two equations in the two variables T and G.
Observe the equations.
If we multiply (2) through out by 5 (to equalise the coefficients of T)and add the resulting equation with (1)thereby getting rid of T and we will arrive at a single equation in the single variable G.
Therefore (2) X5 gives
10G - 5T = 45 ----(3)
3G + 5T = 150 ----(1)
(3) + (1) implies
13G = 195 (learn to add vertically being careful with the signs instead of showing the work of adding left with the left and right with the right and then simplifying!)
G = 195/13 = 13X15/13 = 15
Put G = 15 in (1)
3G + 5T =150
3X15 + 5T = 150
45 + 5T = 150
5T = 150-45
5T = 105
T = 105/5 = 5X21/5 = 21
Therefore Tom is 21 years old.
Verification: Since we have put one value in equation (1) to find the other value, we use the other equation (2) for verificaiton.
(2)is 2G - T = 9 ----(2)
LHS = 2G - T = 2X15 - 21 = 30-21=9 = RHS which is correct
Tom should be 9 years less than twice as old as Gary is.
Of course Tom's age 21 years is 9 less than 30 = twice Gary's age as Gary's age is 15 years

RELATED QUESTIONS
The sum of 3 times Gary's age and 5 times Tom's age is 150. Tom is 9 years less than... (answered by rfer)

gary is 5 years older than henry.21 years ago, gary was twice as old as henry.what is the (answered by mananth)

Gary is as old as Harry will be when Gary is twice as old as Harry was when Gary�s age... (answered by josmiceli)

Tom is 3 times as old as Todd. In 2 years Tom�s age will be 6 years more than 2 times as... (answered by josmiceli)

Three times the sum of Jim�s and Tom�s ages is equal to twelve times the difference of... (answered by josgarithmetic)

The sum of the ages of Tom and Chloe is 72 years. 10 years ago, Tom's age was 3 times... (answered by MathLover1)

Tom is 4 times as old as Todd. In 6 years Tom�s age will be 10 years more than 2 times as (answered by josgarithmetic,MathTherapy)

gary is twice as old as pat. twenty years ago, gary was six times as old as pat. what are (answered by chndnbl)

Judy age now is twice tom's age decreased by 10. In four years, the sum of Judy's age and (answered by josgarithmetic)