Word Problem mixture

[melanie0989]

Programs sell at a baseball game for $2 each, and scorecards sell for $0.75 each. If a total of 200 items was sold (programs and scorecards) for a cash income of $250, how many of each were sold?

The book says the answer is programs=80, scorecards=120

I set up a table and got the formula:

2X+ .75(200-X)= 200(250) but doesn't get me anywhere close to getting the answer so I must of set it up wrong but not sure how to approach the problem.

 

[stapel]

Programs sell at a baseball game for $2 each, and scorecards sell for $0.75 each. If a total of 200 items was sold (programs and scorecards) for a cash income of $250, how many of each were sold?

The book says the answer is programs=80, scorecards=120

I set up a table and got the formula:

2X+ .75(200-X)= 200(250) but doesn't get me anywhere close to getting the answer...

How did you arrive at this equation? What was your reasoning? For what does "X" stand? What "table" did you set up? What were your steps?

For instance, if "the number of programs" is represented by "p" and "the number of scorecards" is represented by "s", what equation represents the total number of items sold? What expression stands for the income earned from selling programs? What expression stands for the income earned from selling scorecards? What equation then stands for the total income?

If you solve the first equation (the one representing the total number of items sold) for one of the variables, and then plug the result into to second equation (the one representing the total income from the items sold), what do you get? When you solve this third equation, what value do you obtain?

Please be complete. Thank you!

 

[lookagain]

Programs sell at a baseball game for $2 each, and scorecards sell for $0.75 each. If a total of 200 items was sold (programs and scorecards) for a cash income of $250, how many of each were sold?

The book says the answer is programs=80, scorecards=120

I set up a table and got the formula:

2X+ .75(200-X)= 200(250) \(\displaystyle \ \ \ \ \) <------ Part of this equation is correct.

but doesn't get me anywhere close to getting the answer so I must of set it up wrong b
ut not sure how to approach the problem.

melanie0989,

one variable is fine, but you have to define what it stands for where it is used in the equation.


Let X = the number of programs.

Then 200 - X = the number of scorecards.

The 250 (dollars) doesn't get multiplied by 200 for the set-up of the equation. That is the
total amount (in dollars) of the programs and the scorecards that were sold.

So, your equation could be:


2X + .75(200 - X) = 250