ksung84 wrote:
Loan X has a principal of $10,000x and a yearly simple interest rate of 4%. Loan Y has a principal of $10,000y and a yearly simple interest rate of 8%. Loans X and Y will be consolidated to form Loan Z with a principal of $(10,000x + 10,000y) and a yearly simple interest rate of r%, where r = (4x+8y)/(x+y). In the table, select a value for x and a value for y corresponding to a yearly simple interest rate of 5% for the consolidated loan. Make only two selections, one in each column.
This is a MIXTURE problem.
A 4% loan (X) is being combined with an 8% loan (Y) to form a CONSOLIDATED loan of 5%.
To solve, we can use ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.
Step 1: Plot the 3 percentages on a number line, with the two starting percentages (4% and 8%) on the ends and the goal percentage (5%) in the middle. X 4%-------------------5%-------------------8% Y
Step 2: Calculate the distances between the percentages. X 4%---------
1--------5%---------
3---------8% Y
Step 3: Determine the ratio in the mixture. The required ratio of X to Y is equal to the RECIPROCAL of the distances in red.
X:Y = 3:1.
Only X=96 and Y=32 yield the required ratio of 3:1.
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