Download Direct Variation

Direct Variation
Direct variation occurs when increasing one item causes something else to
increase in a linear fashion (If two cans of soup cost $6, then four cans of
soup will cost $12).
It does not apply when the increase is irregular (One can of soup costs $3
but if you buy 5 then the sixth one is free).
These problems are almost always set up the same way.
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
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They give you 2 variables (the price of a can of soup and the number
of cans)
They tell you that they vary directly (The cost of soup varies directly
with the number of cans purchased and 2 cans of soup cost $6)
Then they ask you to figure out information about another pair of the
same items.
They could ask you to calculate the cost (How much would 5
cans of soup cost?)
o They could ask you to calculate the number of cans of soup that
you could buy for a certain amount of money (How many cans of
soup could you buy for $12).
o
You always use this equation for direct variation: y = kx
You read the equation as “y varies directly as x” meaning the more of x you
have, the more of y you will have.
There are two steps to solving these problems.
1) First use the equation and the first set of date to find k
The Cost varies directly with the Number of cans of soup:
C = kN
Two cans of soup cost $6:
6 = k(2)
3=k
2) Once you know k, substitute that that and the second set of data into
the equation to find the answer.
How much would 5 cans of soup cost? N = 5
k=3
C = kN
C = 3*5 = 15
Direct Variation
How many cans could you buy for $12?
C = 12
k=3
C = kN
12 = 3N
4=N
There is another way to solve direct variation problems.
Saying that things vary directly is another way of saying that they are
proportional.
It is easiest to remember how to do these problems if you put the same
units in a single fraction and put the numbers that belong together in the
same position.
If 2 cans of soup cost $6, how much will 5 cans of soup cost?
CANS is one unit and DOLLARS is the other. Put CANS in one fraction and
match the DOLLARS with the CANS that are in the corresponding position.
2 cans
$6
=
5 cans
$𝑥
Cross-multiply and solve:
2x = 30
x = 15
If 2 cans of soup cost $6, how many cans can you buy for $12?
2 cans
$6
=
𝑥 cans
$12
Cross-multiply and solve:
6x = 24
x=4