Solving Applied Problems: Algebra

Please solve the following problems:

1. The St. Mark's Community Barbecue 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.

2. 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?

3. An executive nearing retirement made two investments totaling $45,000. In one year, these investments yielded $23430 in simple interest. Part of the money was invested at 4% and the rest at 6%. How much was invested at each rate.

4. 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?

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

6. Starbucks sells cappuccinos in three sizes: tall for $2.65, 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 than the number of grande cappuccinos. If he collected a total of $157, how many cappuccinos of each size did he serve?

7. In a recent year, 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 newspapers ads alone. The amount spent on newspaper ads was $5.1 billion more than what was spent on television ads. How much was spent each form of advertising? I know that the variables represent numbers of billions of dollars.

8. 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 of protein, and 220mg of vitamin C. The dietitian prepares a meal of roast beef, baked potato, and Asparagus according to the info below.
Calories Protein in Grams Vitamin C in milligrams
Roast Beef 3 oz. 300 20 0

Baked Potato 100 5 20

Asparagus 50 5 44mg
180 g

Which meal would you prefer?