The sqaure of tomes age, is 4 times that of his grandmother. When Tom is half as old again as he is now, his grandmother will be 72. How old will tom be when his grand mother is 72? How old his is grandmother now? How do you solve this?
2006-11-23 20:20:15 · 8 answers · asked by Amarilo55 1 in Science & Mathematics ➔ Mathematics
Okay thanks for the answers. But it's slightly confusing as to how you worked it out. Could you make the answer, in a format easier to understand?
-- Erm, i'm not sure what you mean.
2006-11-23 20:44:53 · update #1
When tom is HALF as old as he is NOW
2006-11-23 20:57:36 · update #2
Let the ages be T and G respectively.
T^2 = 4G.
"When T is half as old again..": that means another 0.5T years have passed. So his grandmother is then G+0.5T years old.
So we have T^2 = 4G and G + 0.5T = 72.
Dividing the first one by 4 gives G = 0.25T^2, so substitute that into the second on.
So 0.25T^2 + 0.5T = 72.
Multiplying by 4 and rearranging gives T^2 + 2T - 288 = 0, ie (T-16)(T+18) = 2, so Tom must be 16 years old, and his grandmother 64.
Now, when his grandmother is 72, Tom must be 24.
edit - I'm not sure why you are confused, but I've reworded the above slightly. Note it does *NOT* say 'when Tom is half as old as he is now..', it says 'when Tom is half as old *again*'. Saying half as much again means you add half to the current amount; ie you actually get 1.5 times the current amount.
2006-11-23 20:36:14 · answer #1 · answered by stephen m 4 · 0⤊ 0⤋
Let tomes age be t years
Let his grandmother's age be g years
From first statement:
t^2 = 4.g... (1)
When tom is half as old again, i.e., after t/2 years,
grandmother would be g+t/2 years old.
g+t/2 = 72 ...(2)
Substituting g from (1) into (2),
t^2/4 + t/2 = 72
or t^2 +2t -72*4 = 0
You could solve for t, like any other quadratic equation.
However, i am not clear what you mean by, When Tom is
half as old again. Please clarify.
2006-11-23 20:55:23 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Seems like the easiest way is to multiply 72 by 4, look for perfect squares less than the product, and see if any of their roots fit the other criteria.
72 x 4 = 288
First perfect square less than 288 is 256.
Square root of 256 is 16.
256 / 4 = 64
16 x 1/2 = 8
64 + 8 = 72
Tom is currently 16. His grandmother is 64.
Tom will never be half as old as he is now; the arrow of time doesn't point in that direction.
What the poster means by "half as old again" is adding half Tom's age to his current age.
2006-11-23 20:50:10 · answer #3 · answered by TYPO 1 · 1⤊ 0⤋
If Tom's age now is T and granny's is G,
T^2 = 4G
In T/2 years granny is 72,
so she is now 72 - T/2, or
G = 72 - T/2 and,
T^2 = 4( 72 - T/2),
T^2 = 288 -2T, which yields,
T^2 + 2T - 288 = 0 which factors to
(T + 18)(T - 16) = 0 which means
T = - 18 or T = 16
T = -18 is nonsense, so
Tom is 16, Granny is 64 who will be 72 in 8 years.
2006-11-23 22:56:13 · answer #4 · answered by Robert H 2 · 0⤊ 0⤋
Tom 16, grand ma 64
2006-11-23 20:50:01 · answer #5 · answered by maussy 7 · 0⤊ 0⤋
Hi,
can you clarify, 'When Tom is half as old as he is now, his grandmother will be 72.' This says, "In the future tom will be half as old as he is now."
2006-11-23 20:39:19 · answer #6 · answered by toyallhi 2 · 0⤊ 0⤋
i took the sum as when tom is twiceas old as he is now his grandma is 72
2006-11-23 20:54:51 · answer #7 · answered by raj 7 · 0⤊ 0⤋