Analysis

APPLICATIONS OF SIMULTANEOUS LINEAR EQUATIONS DIRECTIONS: Answer the following problems completely, showing all solutions and/or illustrations when necessary. Write a proper conclusion for each problem. A. Exercise 2D, items 4, 10, 14, 18, and 20 from New Syllabus Mathematics 2 7th Ed. 1) 8 kg of potatoes and 5 kg of carrots cost $28 whereas 2 kg of potatoes and 3 kg of carrots cost $11.20. Find the cost of 1 kg of each item. 2) The figure shows a rhombus with its sides as indicated. Find the perimeter of the figure.

3) Lixin intends to buy either Gift A, which costs $10, or Gift B, which costs $8, as Christmas gifts for each of her parents, 2 siblings, 13 relatives and 10 friends. Given that she intends to spend $230, find the number of each gift she should buy. 4) Two numbers are such that when the larger number is divided by the smaller nuber, both the quotient and the remainder are equal to 2. If five times the smaller number is divided by the larger number, both the quotient and the remainder are also equal to 2. Find the two numbers. 5) Raj has $10. If he buys 8 pears and 5 mangoes, he will be short of $1.10. If he buys 5 pears and 4 mangoes, he will receive $1.75 in change. Find the price of 1 pear and 1 mango. B. Additional Exercises. Answer only the first three problems. 1) Aristotle has a total score of 225 on three Chinese tests. The sum of the scores on the first and second tests exceeds his third score by 61. His first score exceeds his second by 6. Find his average score. 2) A dietitian is preparing a meal consisting foods A, B and C. Each gram of food A contains 2 units of protein, 3 units of fat, and 4 units of carbohydrate. Each gram of food B contains 3 units of protein, 2 units of fat, 1 unit of carbohydrates. Each gram of food C contains 3 units of protein, 3 units of fat and 2 units of carbohydrates. If the meal must provide exactly 25 units of protein, 24 units of fat and 24 units of carbohydrates, how many grams of each type of food should...