teejaycrown wrote:Loan X has a principal of $10,000x and a yearly simple interest rate of 4%. Loan Y has a principal of $10,0000y 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 load. Make only two selections:
21
32
51
64
81
96
In the original problem -- from the IR section of one of the Preptests -- the answer choices appear in a table, as shown here.
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.
4%----------5%-------------------8%
Step 2: Calculate the distances between the percentages.
4%-----
1----5%---------
3---------8%
Step 3: Determine the ratio in the mixture.
The required ratio of X to Y is 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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