Question 1204745: if y varies directly as x, and y=10 when x=7,find y when x=5
Found 3 solutions by josgarithmetic, greenestamps, Edwin McCravy:
Answer by josgarithmetic(39617)   (Show Source):
Answer by greenestamps(13198)  (Show Source):
You can put this solution on YOUR website!
Direct variation means y changes by the same factor as x.
In your example, the x value changes from 7 to 5, a factor of 5/7, so the y value changes by that same factor.
ANSWER: 10*(5/7) = 50/7
Answer by Edwin McCravy(20054)  (Show Source):
You can put this solution on YOUR website!
FORMULA for all "varies ___ as" problems
product of "directly" or "jointly" variables
"Varies ___ as" variable = k* --------------------------------------------
product of "inversely" variables
[If one of the types of variables "directly", "jointly", or "inversely"
variables are missing, always put 1 for them.]
The "varies ___ as" variable is y, so write:
y = k*-----
The only "directly variable" is x, so write it on the top:
x
y = k*----
There is no "inversely variable", so write "1" on the bottom:
x
y = k*-----
1
or
y = k*x
Now we're ready to substitute the numbers for all the letters except the
constant k from this: "y=10 when x=7". Substituting:
10 = k*7
Solve for k:
10/7 = k
Now go back to this equation:
y = k*x
and substitute 10/7 for the constant k.
y = (10/7)*x
Now we substitute x = 5:
y = (10/7)*(5)
Then finish it up:
y = 50/7 = 7 1/7
Edwin
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