solve system of linear equations

4. The St. Marks community bbq served 250 dinners. a child's plate cost 3.50 and an adult's plate cost 7.00. A total of 1347.50 was collected. how many of each type of plate was served?

8. Deep thought granola is 25% nuts and dried fruit. Oat dream granola is 10% nuts and dried fruit. How much of deep thought and how much of oat dream should be mixed to form a 20-lb batch of granola that is 19% nuts and dried fruit?

18. Christina makes a 9.25 purchase at a bookstore in Reno with a 20 bill. The store has no bills and gives her the change in quarters and fifty-cent pieces. there are 30 coins in all. How many of each kind are there?

28. Sally and Rocky travel on motorcycles toward each other from Chicago and Indianapolis, which are about 350km apart, and they are biking at rates of 110km/h and 90km/h. They started at the same time. In how many hours will they meet?

Solve: system in three variables
12. 2x + y + 2z = 11
3x + 2y + 2z = 8
x + 4y + 3z = 0

24. a - 5c = 17
b + 2c = -1
4a - b - 3c = 12

18. solve using the reduced row echelon format(rref) function: show check of the solution
10x + 6y + z = 7
5x - 9y - 2z = 3
15x - 12y + 2z = -5

Solve: system of three equations
2. Starbucks sells cappuccinos in three sizes: tall for 2.63, grande for 3.20, and vente for 3.50. after an outdoor rally for the college football team. Bryce served 50 cappuccinos. the number of tall and vente cappuccinos, combined, was 2 fewer that the number of grande cappuccinos. If he collected a total of 157, how many cappuccinos fo each size did he serve?

12. In recent years, companies spent a total of 84.8 billion on newspaper, television, and radio ads. the total amount spent on television and radio ads was only 2.6 billion more than the amount spent on newspaper ads alone. the amount spent on newspaper ads was 5.1 billion more than what was spent on television ads. how much was spent on each on each form of advertising? ( Hint: let the variables represent numbers of billions of dollars)

16. A dietitian in a hospital prepares meals under the guidance of a physician. Suppose that for a particular patient a physician prescribes a meal to have 800 calories, 55g protein, and 220mg of vitamin c. the dietitian prepares a meal of roast beef, baked potato, and asparagus according to the data.
roast beef 3oz: 300 calories, 20 g protein, and 0 mg vitamin c
baked potato: 100 calories, 5 g protein, and 20 mg vitamin c
asparagus 180 g: 50 calories, 5 g protein, and 44 mg vitamin c

how many servings of each food are needed in order to satisfy the doctor's order.
Which meal would you prefer eating?

Solve: break-even analysis, for each of the following pairs of total-cost and total-revenue functions, find
(a) the total profit function and (b) the break-even point.
4. C(x) = 30x + 49,500; R(x) = 85x