By selling old cd's, sarah has a store credit card for $153.a new cd costs $18 .what are the possible numbers of new cd's sarah
1 answer:
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Answer:
C. Yes, 3.5.
Step-by-step explanation:
If there is a relationship of direct proportionality for every ordered pair of the table, then the constant of proportionality must the same for every ordered pair. The constant of proportionality () is described by the following expression:
(1)
Where:
- Input.
- Output.
If we know that ,
and
, then the constants of proportionalities of each ordered pair are, respectively:
Since , the constant of proportionality is 3.5.
Our goal here is to somehow "surgically remove" the repeating part of the number, so let's start by putting the original value in a variable and messing around with it a bit.
We'll let . We want to cut the
bit off completely, so let's create the scalpel that'll let us do that. If
, then we can also say that
. Maybe I was lying a bit: the
is our real scalpel here, and
is where we'll be making the cut. Mathematically, a "cut" is almost always shorthand for subtraction, so let's see what our operation (cutting
off of
) leaves us with:
The operation was a success! We can now simply divide either side by 9 to find , which, when reduced by dividing the numerator and denominator by 3, gives us