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Peter, a loan officer at a bank, has 1,000,000 to lend and is required to obtain an average return 18 percent per year. If he can lend at the rate of 19 percent or at the rate of 16 percent, how much can he lend at the 16 percent rate and still meet his requirement?
I get lost with so many percents.
Do I really ned to use all the percents given?
For example, 16% is given twice in the question to confuse the student, right?
[I'd say that some exercises in the textbooks, usually word problems, are out to confuse the students. Words!]Quote:
Originally Posted by symmetry
I understand the Question as if Peter were to lend the 1 Million into two parts, one earning 19 percent and the other 16 percent, he might get his target of average 18 percent earnings. Find the part that is to be loaned at 16 percent.
Let x = part to loaned at 16 percent.
So, 1,000,000 -x = part at 19 percent.
(16% of x) +(19% of (1,000,000 -x)) = 18% of !,000,000
(0.16)(x) +(0.19)(1,000,000 -x) = (0.18)(1,000,000)
0.16x +190,000 -0.19x = 180,000
0.16x -0.19x = 180,000 -190,000
-0.03x = -10,000
x = (-10,000) / (-0.03)
x = 333,333.33
So, Peter must lend 333,333.33 at 16% (and 666,666.67 at 19%) to meet his requirement of an average of 18% from the 1 Million. ----answer.
Check,
(0.16)(333,333.33) +(0.19)(666,666.67) =? (0.18)(1,000,000)
53,333.33 +126,666.67 =? 180,000
180,000 =? 180,000
Yes, so, OK.
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[Going to sleep now.]
I can clearly see that no matter how much I try to avoid dealing with setting up equations for certain math word problems, this is a must depending on the question's level of difficulty.