Kyle works at a donut factory where a 10 oz cup of coffee costs $0.95, a 14 oz cup cost $1.15, and a 20 oz cup cost $1.50. So let's let X be amount of 10 oz cups, Y equal amount of 14 oz cups, and Z be the amount of 1014 and 20. So it talks about there's a total of 29 cups, so X + Y + Z is going to equal 29. And then it talks about $0.95. So $0.95 for each X cup and $1.15 for each Y cup and $1.50 for each Z cup is going to equal the total of 3580. So money plus money plus money equal total money. The last equation is going to come from the oz. So there are 10 ounces in each X cup, there's 14 ounces in each Y cup, and there's 20 ounces in each Z cup. And there was 444 oz total used. So I might take and simplify some of these equations. This top or the second one I might multiply everything through by 100. So 95X plus 115 Y plus 150Z equal 3580. Now, I like small numbers if I can, and those are obviously all divisible by 5, so I might go ahead and divide everything 3 by 5 S 95 / 5 is 19, and five goes into 11 twice with one leftover, SO23Y5 goes into 150. Thirty times five goes into 3575 goes into eight once with three leftover, so five goes into 36. So this is going to be my new equation 2. Looking at equation 3, I might realize that those are all divisible by two. So 5X plus seven y + 10 Z equal 222. So that's going to be my new equation 3. And then I still have that original equation one that was X + y + Z equal 29. So when I look here, I want to look for small numbers and I want to look for numbers that would be easily combinable. So I think I'm going to do the ZS because 30 and 10 and one is going to be pretty reasonable. So if we look here and we do, let's start with one and two, so one and two, we do one and two, we're going to multiply 1 by -30 so -30 X -30 Y -30 Z equal negative O 726870. And then if we leave equation 2 alone, we can see that those Z's are going to cancel and we're going to get -11 X -7 Y equaling -154. And this is going to be my new equation 4. So now I have to use equation 3 and I might use 3 with one multiplying 1 by -10 so -10 X -10 Y -10 Z equal -290 and three was 5X plus seven y + 10 Z equal to 22. So we get -5 X -3 Y equaling -68, and this is our equation 5 S. Now equations four and five had the same variables, so four and five. And we get -11 X -7 Y equal -154 and -5 X -3 Y equal -68. Now I need additive inverses. So I think what we'll do is we'll use the YS because the numbers are smaller. I'm going to multiply this top equation by -3 and I'm going to multiply the bottom 1 by 7. So -3 is going to give me 30 three X + 21 Y equal two carry 156462. Then if I multiply the bottom 1 by 7 I get -35 X -21 Y equal 168 * 7 seven times 8 68 * 7. I don't like 8476, OK, And that's going to be a negative. So then when we add here, we get -2 X, the YS cancel and we get negative 14. So X is going to be 7. Once I get X, I'm going to substitute it into four or five, and it doesn't matter which. I'm going to use 5 just because the numbers are a little smaller -5 * 7 - 3 Y equal -68 so -35 - 3 Y equal -68 negative 3 Y equal 3/3 negative 33, so Y is 11. Once I get X&Y, I'm going to substitute it back into any of the originals. I'm going to use One X + y + Z equal 29, so 7 + 11 + Z equal 2918 + Z equal 29 Z equal 11. So there were seven cups of the 10 oz and 11 of the 14 oz and 11 also of the 20 oz.