A movie rental store sells a couples movie pack for six dollars and a family movie pack for ten dollars. In one year, the Nguyen family paid one hundred and fourteen dollars for 13 movie packs. How many family movie packs did they pay for?

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Question

A movie rental store sells a couples movie pack for six dollars and a family movie pack for ten dollars. In one year, the Nguyen family paid one hundred and fourteen dollars for 13 movie packs. How many family movie packs did they pay for?

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conqueror · Answer

@IMStuck

anonymous · Answer

12

imstuck · Answer

I will show you how to figure this out.  although you may have been given the correct answer, if you don't know how to come to it on your own, all the right answers in the world don't help, do they?

imstuck · Answer

Ok, this works out as a system of equations involving 2 unknowns, an x and a y, let's call them.  Let's let x = a couple's pack and y = a family pack.

imstuck · Answer

We are told that a couple's pack cost $6 and a family pack cost $10.  We also know that the family bought a total of 13 packs (we don't know which ones they bought, though.  At least not yet!) and paid $114 for those packs.

imstuck · Answer

We have two different things going on here now.  We have the number of packs the family bought in one equation, and then the money they spent on those packs in another equation.  So let's relate the number of packs to one another first. We don't know how many couple's packs they bought or how many family packs they bought, only that they bought a total of 13 of them. So couple's packs + family packs = 13 packs, OR x + y = 13.  That's our first equation.

imstuck · Answer

The second equation has to do with money.  A couple's pack costs $6.  But if you don't know how many they bought, in order to assign a variable to it, you say 6x.  6 being the cost of a couple's pack, and x being the number they bought, which is what you are looking for.  Do the same with the family pack cost.  That would be 10y, the 10 being the cost for one family pack and y being the number of family packs bought.  We know they spent $114 total.  So our equation relating these money terms would be the number of $6-packs + the number of $10-packs = $114.  OR 6x + 10y = 114.  Now we have two equations.

imstuck · Answer

x +     y =  13
  6x + 10y = 114  do you know how to solve a system of equations that looks like this?