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
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