Question 1170564: Dave is x years old his sister is 5 years older his father is 5 times older than dave what age is dave
Found 4 solutions by ikleyn, Theo, greenestamps, josgarithmetic:
Answer by ikleyn(52776)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! there could be multiple answers to this questions the way it is presented.
for example:
when the father is 20, dave is 4 and his sister is 9.
when the father is 25, dave is 5 and his sister is 10
when the father is 30, dave is 6 and his sister is 11.
when the father is 35, dave is 7 and his sister is 12.
etc.....
in other words, there are multiple answers to this problem as it is presented.
please check the problem again to see if there is something missing.
usually there is something that allows you to pin one of the variable to a specific age, like:
today his father is 5 times as old as he is.
in 5 years, his father is 4 times as old as he is.
this leads go two equations that need to be solved simultaneously.
they would be:
y = 5x
y+5 = 4*(x+5)
you would simplify the second equation to get:
y + 5 = 4x + 20
you would then replace y with 5x to get:
5x + 5 = 4x + 20
you would then solve for x to get:
x = 15
when x = 15, y = 75
y + 5 = 80 and x + 5 = 20
75 is equal to 5 * 15.
80 is equal to 4 * 20.
the problem was able to be solved to a specific value.
a key factor is that the value of y and the value of x in both equations need to represent the same thing.
in the equation just solved, y represented his father's age and x represented his age.
you could have said there were two equations, such as:
y = x + 5
y = 5x
unfortunately, now y represents two different values.
the y in the first equation represents his sister's age.
the y in the second equation represents his father's age.
these equations could not be solved simultaneously for that reason.
if you did try to solve these equations simultaneously, you would replace y with x + 5 to get:
x + 5 = 5x
you would then subtract x from both sides of the equation to get:
5 = 4x
you would then solve for x to get:
x = 5/4.
you would then replace x with 5/4 in your two original equations to get:
y = x + 5 becomes y = 5/4 + which gets you y = 25/4 = 6 and 1/4.
y = 5x becomes y = 5 * 5/4 which gets you y = 25/4 = 6 and 1/4.
you have a solution, but the solution means:
y = his sister's age.
y = his father's age.
since they can't be the same age, then the solution is invalid.
the equation is invalid because all instances of y have to represent the same thing in both equations and all instances of x have to represent the same thing in both equations.
x is ok because it represents dave's age in both equation.
y is not ok because it represents his sister's age in one equation and his father's age in the other equation.
if you have any questions, let me know.
theo
Answer by greenestamps(13198)  (Show Source):
You can put this solution on YOUR website!
The statement of the problem is flawed, because no information is given about the actual ages, or the sum of the ages. That makes it impossible to find a solution.
If the sum of the ages had been given, the problem would still be flawed, because of the use of the phrase "his father is 5 times older than Dave".
Nearly always, a casual reader interprets "5 times older than" to be the same as "5 times as old as". But they are different.
If an age is x, then the age that is 5 times AS OLD AS x is clearly 5 times x, or 5x.
But if an age is x, then the age that is 5 times OLDER THAN x is x, plus 5 times MORE x, which is x+5x = 6x.
The phrase that says one age is n times OLDER than another age should never be used in the statement of a math problem, because the meaning is probably not what the author of the problem intended.
Answer by josgarithmetic(39616)  (Show Source):
You can put this solution on YOUR website! Some punctuation is needed but,
The description allows you to do something like so:
Dave x
Sister x+5
Father 6x
There are values for x which will make sense.
The problem is open-ended, or possibly incomplete.
That is all.
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