i am having some trouble with math and i need a detailed explanation ?!

Question

:

 Julie and Pete are selling fruit for a school fundraiser. Customers can buy boxes of oranges and boxes of lemons. Julie sold 2 boxes of oranges and 3 boxes of lemons for a total of $83. Pete sold 3 boxes of oranges and 3 boxes of lemons for a total of $96. What is the cost of one box of lemons?

Answer 1

You have two variables with unknown values. You cannot solve this with a single equation, because one answer would be dependent upon the other. But this can be solved with a two equation system. By using two equations, one of the variables can be eliminated. You solve for the remaioning variable, and then use that answer to solve for the other one.

There are two approaches to this type of problem, elimination or substitution. In either case, the first step is to take the information and write two equations. Let's make L = the price of lemons, and R = the price of oranges (O looks too much like zero, so not the best vriable choice).

Julie sold 2 boxes of oranges and three boxes of lemons for a total of $83. Turning that into an equation gives us:

2R + 3L = 83

Pete sold 3 boxes of oranges and 3 boxes of lemons for a total of $96. The equation for that would be:

3R + 3L = 96

We can eliminate the L variable by subtracting Julie's equation from Pete's equation:

3R + 3L = 96

-2R + 3L = 83

R = 13

Now plug that into one of the original equations and you get:

3R + 3L = 96

(3 x 13) + 3L = 96

39 + 3L = 96

3L = 57

L = 19

In this case, it was easy to eliminate the L variable because they both sold the same amount of lemons. But it is not always that easy. You should also be able to solve these kind of problems using substitution. For that method you use one of the equations to solve a variable in terms of the other. Then you plug that value into the other equation and solve. Let's try that:

Again, the two equations:

2R + 3L = 83

3R + 3L = 96

Let's use the second equation to solve R in terms of L:

3R + 3L = 96, divide both sides by 3:

R + L = 32, subtract L from both sides:

R = 32 - L, substitute For R in the first equation (you have to use the equation you have not used yet)

2R + 3L = 83

2 (32 - L) + 3L = 83, distribute the 2:

64 - 2L + 3L = 83, combine terms:

64 + L = 83, subtract 64 from both sides:

L = 19

Now substitute L = 19 for R in either original equation and solve for R

2R + 3L = 83, substitute

2R + 3(19) = 83, simplify

2R + 57 = 83, subtrsct 57 from both sides:

2R = 26, divide by 2

R = 13

So you get the same answer either way. It is good to know both methods because sometimes one method is complicated to use with the equations you have, but the other method might be easier.

Hope this helps

Answer 2

Yeah, I wasn't very good with these at first. Let's do this.

2o + 3l = 83

3o + 3l = 96

So, I'll start off by noting that Pete sold one more box of oranges than Julie snd his total was $13 more, so that means that one box of oranges sells for $13.

2(13) + 3l = 83

26 + 3l = 83

3l = 57

l = $19

Now, let's say that didn't occur to you like it did to me. We could solve another way.

3l = 83 - 2o

3l = 96 - 3o

Well, if 3l has two "values" then they are equal!

83 - 2o = 96 - 3o

o = 13

Continue aand solve for l.

There are a couple of other ways to solve, but I'll stop there.