Question 1007090: Translate the following situation into an equation. Do not solve.
“Sarah is three times as old as Sam and Mark is eight years younger than Sam. If their average age is 44, how old is Sarah?”
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x = sarah's age.
y = sam's age.
z = mark's age.
“Sarah is three times as old as Sam and Mark is eight years younger than Sam. If their average age is 44, how old is Sarah?”
x = 3y (sarah is three times as old as sam).
z = y - 8 (mark is 8 years younger than sam).
(x + y + z)/3 = 44 (their average age is 44).
how old is sarah?
make sure that when you get a solution that you confirm it to be true by checking it against the original requirements.
if you run into great difficuty finding a solution, let me know and i'll show you how i did it.
fyi, you can set up 3 variables and then work on figuring out equivalencies.
another way is to work with one variable directly, such as the following:
“Sarah is three times as old as Sam and Mark is eight years younger than Sam. If their average age is 44, how old is Sarah?”
x = sam's age.
3x = sarah's age.
x - 8 = mark's age.
or:
x = sarah's age.
x/3 = sam's age.
x/3 - 8 = mark's age.
or:
x = mark's age.
x + 8 = sam's age.
3(x+8) = sarah's age.
if the average of their ages is 44, then the total of their ages will be 44 * 3 = 132.
in the first method you would get x + y + z = 132.
in the second and third and fourth methods, you will get:
x + 3x + x - 8 = 132 (second method)
x + (x/3) + (x/3) - 8 = 132 (third method)
x + x + 8 + 3 * (x + 8) = 132 (fourth method).
all 4 methods will give you the same answer.
just be careful as to whose age x represents.
sometimes i solve them directly as in the second through fourth method.
sometimes i solve them indirectly as in the first method.
it depends on the problem and how complex the equations become.
the first method has advantages in clarity of presentation even though it involves more variables to start wtih.
the trick is to reduce the number of variables to a number that can be solved either directly or indirectly.
the general rule for solving directly is that the number of unknown variables and the number of equations should be the same.
translating the word problem to equations is a most important part of solving these types of problems.
with practice it gets easier.
assigning a variable to an unknown quantity is the first part.
fyi, the solution that i got was:
sarah = 84
sam = 28
mark = 20
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