Question 1122104
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Here is an alternative to the standard algebraic solution method shown by the other tutor.  If you understand this method, it will get you to the answer much faster and with less work than the algebraic method -- especially if you are good with some mental arithmetic.<br>
To show you how fast the solution process can be, I'll first just show you the calculations that are required; then I will explain the process.<br>
(1) 3800*.035 = 133; 3800*.06 = 228
(2) 228-188 = 40; 188-133 = 55
(3) 40:55 = 8:11
(4) (8/19)3800 = 8*200 = 1600; (11/19)3800 = 11*200 = 2200
(5) Answer: $2200 at 6%; $1600 at 3.5%.<br>
In the first three steps, we determine the ratio in which the money needs to be split by comparing the actual amount of interest to the amounts of interest if all the money had been invested at each of the two rates.
Step 1: determine the amounts of interest if all the money were invested at each of the rates.
Step 2: find how far the actual interest amount is from each of the amounts in step 1.
step 3: express the distances that the actual amount of interest is from the two amounts in step 1 as a ratio.<br>
That ratio ratio is the ratio in which the money needs to be split between the two accounts.  The actual interest is closer to $228 than to $133, so the larger portion needs to be invested at the higher rate.
Step 4: convert the ratio into two fractions that are the fractions of the total that needs to be invested at each rate; multiply the total amount by each of those two fractions to find the amounts that need to be invested at each rate.