Formulate but do not solve the problem. Mr. and Mrs. Garcia have a total of $125,000 to be invested in stocks, bonds, and a money market account. The stocks have a rate of return of 11%/year, while the bonds and the money market account pay 8%/year and 4%/year, respectively. The Garcias have stipulated that the amount invested in the money market account should be equal to the sum of 15% of the amount invested in stocks and 20% of the amount invested in bonds. How should the Garcias allocate their resources if they require an annual income of $11,000 from their investments? (Let x, y, and z denote the amount, in dollars, in stocks, bonds, and money markets, respectively.) = 125,000 = 11,000 =z
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
The Johnson Farm has 500 acres of land allotted for cultivating corn and wheat. The cost of cultivating corn and wheat (including seeds and labor) is $44 and $30 per acre, respectively. Jacob Johnson has $17,800 available for cultivating these crops. If he wishes to use all the allotted land and his entire budget for cultivating these two crops, how many acres of each crop should he plant? (Let x and y denote the number of acres of corn and wheat, respectively.)
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Solve the system of linear equations using the Gauss-Jordan elimination method.
| 2x | + | 4y | − | 6z | = | 42 |
| x | + | 2y | + | 3z | = | 3 |
| 3x | − | 4y | + | 4z | = | −16 |
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