Intermath: Investigations: Number Concept: Integers
At Gardner's Gourmet Candies, a package of gummy bears cost 13 cents less than caramels and 28 cent more than jaw breakers. You can buy one of each for a total of $6.39. How many cents does one package of gummy bears cost?
The trick to understanding this problem is to make an equation. First, what do we know? 1) gummy bears cost 13 cents less than caramels. So if we made that into a math equation, we would have gb + 13 = c. Maybe that seems backwards, were you thinking gb - 13 = c? Rembers the property of equality - or what it means for two things to be equal! If gummy bears cost 13 cents less, then to make their cost equal to caramels, you need to add 13 cents. 2) gummy bears cost 28 cents more than jaw breakers. Let's make an equation for this too. So in order to make the price of gummy bear equal to jaw breakers, we need to take away 28 cents from the cost of the gummy bears. Now, your thinking . . . gb - 28 = jb. AND 3) the cost of one package of gummy bears, caramels, and jaw breakers is $6.39. Making an equation for this is as simple as it seems . . . gb + c + jb = $6.39.
Now let's take everything we know:
gb + 13 = c; gb - 28 = jb, and gb + c + jb = 6.39
Do you notice any constistencies in each equation? Each equation has the term gb or gummy bears. We can use that to our advantage. In the last equation, the first term is gb, and the second is c. Instead of writing c, what else could I write? Or what is equivalent to c? gb +13! Now we can say
All I did was remove the c and put an equivalent expression in its place. We can do the same for the final term in that equation. (This time I am going to write the cents as fractions of a dollar.
Now all we have to do is solve.
So three packs of gummy bears is $6.24. But the question asks how much one costs. We can find that by dividing 6.24 by 3, which gives the cost for an individual package.
Now we have an answer. One package of gummy bears costs $2.08. That's pretty expensive if you ask me.