Question 696191: a shipping company charges a flat rate of $5.00 plus an additional $0.65 per pound to ship a package. what equation can be used to find the total cost in dollars, c, for shipping a package that weighs x pounds?
Answer by RedemptiveMath(80)   (Show Source):
You can put this solution on YOUR website! Let us analyze this problem piece by piece. Essentially, we'll need to convert English language into mathematical language (i.e. equations). Let us begin.
"...charges a flat rate of $5.00..." Flat rates in the business world is what we call constants in the mathematical word. That is, if we have a flat rate, that number doesn't change for anything because it has no variable attached to it (unless otherwise noted). You can identify what the constants are because they do not have the tags "per", "each", or "for every" attached to them when in the English language. In this case, this number remains the same no matter if 1 package gets shipped or a 1000 packages get shipped. So, we have the first part of our equation:
$5.00...
"...plus an additional $0.65 per pound to ship a package." This lets us know where our first variable will be. We can identify where the variables will be when we see the words "per" or the like pop up. The word "per" can roughly translate to multiplication in math terms. What two things are being multiplied then? We have an amount, $0.65, and we have "pound". Usually the two things we need to multiply are right next to each other in the sentence (separated by "per", "for every" and so forth). We don't know the "pounds", and the problem tells us to use "x" in place of the pounds. So, we have $0.65 * x (65 cents times x), or $0.65x. (We don't have to use a multiplication symbol because there is no ambiguity between the expressions). Notice the word "plus" that begins the sentence fragment we are currently dealing with. This means that whatever is before the word "plus" is being added to whatever is after. We have already established that $5.00 is before, so we continue writing our equation:
$5.00 + $0.65x...
There is no more information about what the charges would be for shipping packages. We have the constant rate of $5.00, and we have the rate of $0.65 per pound. Since we are given no more information, the part of the equation we have so far must be what the total cost equals. We can now finish our equation:
$5.00 + $0.65x = c.
C would be the total cost. The total cost is obviously dependent on what x equals. If there are more pounds being shipped, then the total cost rises. If there are less pounds being shipped, the total cost drops. We can rewrite the equation if we want the variable to come first (conventional):
$0.65x + $5.00 = c.
It doesn't matter which way you add the two things on the left side of the equation in the sense of getting the same answer. For example, if you have 3 + 4, you know the answer is going to be 7. You could write 3 + 4 = 7. You also know that 4 + 3 also equals 7. You could write it as 4 + 3 = 7. 3 + 4 = 7 and 4 + 3 = 7 are equivalent statements. They have the same terms and the same answer. However, it is proper to write it the way directly above.
|
|
|
