You invest in AAA-rated bonds, A-rated bonds, and B-rated bonds. The average yields are 4.5% on AAA bonds, 5% on A bonds, and 9% on B bonds. You invest twice as much in B bonds as in A bonds. Let x, y, and z represent the amounts invested in AAA, A, and B bonds, respectively. x + y + z = (total investment) 0.045x + 0.05y + 0.09z = (annual return) 2y − z = 0 Use the inverse of the coefficient matrix of this system to find the amount invested in each type of bond for the given total investment and annual return. (Round your answers to the nearest cent.) Total Investment Annual Return $12,800 $885 amount invested in AAA-bonds $?? amount invested in A-bonds $ ?? amount invested in B-bonds $ ???
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.
You invest in AAA-rated bonds, A-rated bonds, and B-rated bonds. The average yields are 4.5% on AAA bonds, 5% on A bonds, and 9% on B bonds. You invest twice as much in B bonds as in A bonds. Let x, y, and z represent the amounts invested in AAA, A, and B bonds, respectively.
| x | + | y | + | z | = | (total investment) |
| 0.045x | + | 0.05y | + | 0.09z | = | (annual return) |
| 2y | − | z | = | 0 |
Use the inverse of the coefficient matrix of this system to find the amount invested in each type of bond for the given total investment and annual return. (Round your answers to the nearest cent.)
| Total Investment | Annual Return | |
|---|---|---|
| $12,800 | $885 |
| amount invested in AAA-bonds | $?? |
| amount invested in A-bonds | $ ?? |
| amount invested in B-bonds | $ ??? |
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