Section 3.6 Systems of Linear Equations in Three Variables and Applications 291 17. 18. 19. 20. 21. 22. Concept 3: Applications of Linear Equations in Three Variables 3x 2z 11 y 7z 4 x 6y 1 4x 9y 8 8x 6z 1 6y 6z 1 x y 3z 2 2x 3z 5 3y 3z 2 2x 3y 2z 1 x 2y 4 x z 1 x y z 11 x y z 15 2x y z 9 x y z 6 x y z 2 2x 3y z 11 23. A triangle has one angle that measures 5 more than twice the smallest angle, and the third angle measures 11 less than 3 times the measure of the smallest angle. Find the measures of the three angles. (See Example 2.) 24. The largest angle of a triangle measures 4 less than 5 times the measure of the smallest angle. The middle angle measures twice that of the smallest angle. Find the measures of the three angles. 25. The perimeter of a triangle is 55 cm.The measure of the shortest side is 8 cm less than the middle side.The measure of the longest side is 1 cm less than the sum of the other two sides. Find the lengths of the sides. 26. The perimeter of a triangle is 5 ft.The longest side of the triangle measures 20 in. more than the shortest side.The middle side is 3 times the measure of the shortest side. Find the lengths of the three sides in inches. 27. Sean kept track of his fiber intake from three sources for 3 weeks.The first week he had 3 servings of a fiber supplement, 1 serving of oatmeal, and 4 servings of cereal, which totaled 19 g of fiber.The second week he had 2 servings of the fiber supplement, 4 servings of oatmeal, and 2 servings of cereal totaling 25 g.The third week he had 5 servings of the fiber supplement, 3 servings of oatmeal, and 2 servings of cereal for a total of 30 g. Find the amount of fiber in one serving of each of the following: the fiber supplement, the oatmeal, and the cereal. (See Example 3.) 28. Natalie kept track of her calcium intake from three sources for 3 days.The first day she had 1 glass of milk, 1 serving of ice cream, and 1 calcium supplement in pill form which totaled 1180 mg of calcium.The second day she had 2 glasses of milk, 1 serving of ice cream, and 1 calcium supplement totaling 1680 mg.The third day she had 1 glass of milk, 2 servings of ice cream, and 1 calcium supplement for a total of 1260 mg. Find the amount of calcium in one glass of milk, in one serving of ice cream, and in one calcium supplement. 29. Goofie Golf has 18 holes that are par 3, par 4, or par 5. Most of the holes are par 4. In fact, there are 3 times as many par 4s as par 3s.There are 3 more par 5s than par 3s. How many of each type are there? 30. Combining peanuts, pecans, and cashews makes a party mixture of nuts. If the amount of peanuts equals the amount of pecans and cashews combined, and if there are twice as many cashews as pecans, how many ounces of each nut is used to make 48 oz of party mixture? 31. Souvenir hats,T-shirts, and jackets are sold at a rock concert.Three hats, two T-shirts, and one jacket cost $140.Two hats, two T-shirts, and two jackets cost $170. One hat, three T-shirts, and two jackets cost $180. Find the prices of the individual items.
miller_intermediate_algebra_4e_ch1_3
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