Video Transcript
In 1995, music stores sold cassette
tapes for two dollars. Write an equation to find 𝑡, the
total cost in dollars for buying 𝑐 cassette tapes, and then find out how much it
would cost to buy three cassette tapes.
In this question, we’re given the
information about the cost of a cassette tape. The next part of this question
might seem quite confusing. We’re told to write an equation to
find 𝑡, the total cost in dollars, for buying 𝑐 cassette tapes. So let’s break this down. We’re told that one cassette tape
would cost two dollars, which means that two cassette tapes would cost four dollars
and three cassette tapes would cost six dollars and so on.
So how about if we bought 𝑐
cassette tapes where we don’t know the value of 𝑐? How much would that cost? Well, each cassette tape is still
going to cost two dollars. So the total cost would be two
times 𝑐 dollars or simply two 𝑐 dollars. We could then say that the total
cost would be two 𝑐 dollars. But, however, we were asked to find
𝑡, the cost in dollars. This means that we need to replace
the wording of total cost with 𝑡. We can also get rid of the dollar
sign as we’re told that 𝑡 is the cost in dollars. We have now written an equation in
the variables of 𝑡 and 𝑐.
Notice that the two in this
equation represents the cost of each cassette and its constant. If we compare this to the linear
function 𝑦 equals 𝑚𝑥 plus 𝑏, then we might notice that we don’t have any
𝑏-value. If we were to graph this function
of 𝑐 against 𝑡, then the graph would look like this. The slope of the line would be two
as one cassette tape costs two dollars. And the 𝑦-intercept would be zero
because if we bought zero cassette tapes, it would cost us zero dollars which is why
the 𝑏-value in the linear function form is zero. Now that we found our equation,
we’re asked for one more thing, the cost of buying three cassette tapes.
We can use our equation plugging in
the value of 𝑐 equals three. This would give us 𝑡 equals two
times three, which of course would give us six, which means that three cassette
tapes would cost six dollars. We can then give our two
answers. The equation we found is 𝑡 equals
two 𝑐 and the cost of three cassette tapes is six dollars.
