What does this mean by system of equations and can you write down the equations so I can see an example?

Question

Drew is a counselor at a summer camp and need to buy prizes for the competitions at the end of the week.

:There are two groups, middle school,high school, for which needs prizes

:He wants to buy at least 14 prizes, but to spend no more than 50.

:Drew finds fun middle school prizes for $2 each and high school for $3 each.

Which system of equations describes the number of middle school prizes(x) and number of high school prizes(y) that Drew can purchase?

Is one equation 2x+3y less than or equal to 50

and the other is x+y greater than or equal to 14

I'm not sure if this is correct, but I'm confused on what the question means...

Answer 1

The question is really just asking you to do a part of the problem, instead of the entire problem. Generally, when solving a word problem like this you would perform the following steps:

1. Identity and label relevant variables. In this case, it seems that you have chosen x and y for your variables, which represent the number of middle school prizes to buy and the number of high school prizes to buy, respectively.
2. Determine how the variables are related. This involves translating any sentences in the word problem which involve the variables you picked from the first step into equations (or inequalities). In this case, you have correctly identified that the inequalities are 2x + 3y ≤ 50 and x + y > 14.
3. Solve the equations and/or inequalities from the previous part.

Now, this particular question is only asking you to find the system of equations which represent how to find the variables x and y. So, in this case you would stop at Part 2. This problem is really asking you to set up the problem, instead of completely solving it.

Answer 2

Yes, you are correct.

It is usually helpful to specify what your variables represent...and sometimes to use letters that remind you of the meaning of each. For example, M for # middle school prizes and H for # of high school prizes.