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I'm trying to figure out and understand this word problem, which requires system of equations. The word problem is below:

Two companies, Ben's computers, and Jerry's computers, both produce computers and sell them to a school. Jerry's computers are selling for 200 more than Ben's computers because they offer a little better computer. Ben's computers is charging $1500 for each computer. The total number of computers ordered by the school is 170. Ben's computers sells 20 more than twice the number of computers than Jerry's computers sells to the school.

The school need to know how many computers each company sell to the school? The school also needs to know what their total cost will be.

This is driving me crazy, any help is appreciated!

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    $\begingroup$ Yes there will be simultaneous equations. The first thing to do is to come up with variables for the various items. The second will be to write equations, using the variables you defined, that correspond to the statements in the second paragraph. Why don't you start with the first step (it should be easy)? And then make an attempt at the second step. Update the OP with what you come up with. $\endgroup$
    – Χpẘ
    Commented May 12, 2017 at 0:14

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When reading a word problem like this, just keep your head calm and write down every piece of information in a mathematical form.

Reading the problem, we see that there are two companies, Ben's and Jerry's company. Both of them sell some amount of computers for the school. Also the prices are important here. Therefore, let's mark:

  • Ben's sells $x$ computers, price is $s$
  • Jerry's sells $y$ computers, price is $t$

We see the sentence "Jerry's computers are selling for 200 more than Ben's computers"; which means that

$$ t = s + 200 $$

Next, we have "Ben's computers is charging 1500 for each computer", which simply means

$$ s = 1500 $$

Next information is "The total number of computers ordered by the school is 170", which is translated as $$x+y = 170$$. The last sentence, the toughest one, is "Ben's computers sells 20 more than twice the number of computers than Jerry's computers sells to the school", which means

$$ x = 20 +2y $$

To answer the question, we need to find out $x$ and $y$, as well as the value of the expression $xs + yt$, which is the total price.

In order to solve for $x$ and $y$, we can write the two equations like this: $$ \left\{ \begin{array}{cc} x + y & = 170 \\ x - 2y &= 20 \end{array} \right. $$

Subtracting the two equations results in $3y = 150 \Rightarrow y = 50$. Inserting this into the first equation, we can solve $x = 120$. The prices are easy, $s = 1500$ (known) and $t = s + 200 = 1500 + 200 = 1700$. Therefore, the total cost of buying the computers is $(120)(1500)+(50)(1700) = 265,000$.

The final answers are, therefore,

  • Ben's sells 120 computers and Jerry's sells 50 computers
  • The total cost is 265,000 dollars.
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