[I'd say that some exercises in the textbooks, usually word problems, are out to confuse the students. Words!]

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.]