One evening, 1500 concert tickets were sold for the Fairmont Summer Jazz Festival. Tickets cost $25 for covered pavilion seats and 15 for lawn seats. The total receipts were 30,500. How many tickets of each type were sold? So the first thing we're going to do is define our variables. Let's let X be the amount of pavilion seats and Y be the amount of lawn seats. So we know the total amount was 1500 or X + Y equal 1500. We also know the total money brought in was 30,500, so 25X plus 15 Y equal 30,500. Now we're going to use elimination to solve for the two unknowns. If we start by looking at getting rid of the X's, we would multiply this top equation 3 by -25, because we need to get additive inverses for the coefficients on the X term. So if X is if that top equations multiplied by -25, we'd have a negative 25 X and a +25 X when we add them. So just multiplying it through, we get -25 X -25 Y equaling -37,500. If we add that to the other equation 25X plus 15 Y equal 30,500, we get -10 Y equaling -7000 divide each side by -10 so y = 700. Now I want to go back and do the same thing, but this time we're going to eliminate the YS. So if I'm going to get rid of the Y's -15 Y is going to be my additive inverse. So I'm going to multiply this top one through by a -15 so I get -15 Y and +15 Y. When I add those two equations together I get 10X equaling 8000 or X is 800. Now story problems have five steps. One is to define your variables 2 set up the equations three solve. So we're only 3/5 of the way through with this equation. The 4th step is to check it. Does 800 + 700 equal 1500? Yes, we have to check it in both equations because just it may be true in one but may not be true in the other. So we're going to check in both equations 25 * 800 + 15 * 700 = 30,500. That one checks the check of step four in a story problem. The 5th step is to answer what was asked for. If we go back up to the original, it's asking how many tickets of each type were sold. So there were 800 pavilion seats and 700 lawn seats sold. If a problems asked for in words, our answer should always be a response in words. If our problems ask for numbers, then it's OK to have our response be numbers.