1953 AMC 12 Problem 17

Attempt Problem 17 of the 1953 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1953 AMC 12 solutions, or check the answer key.

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17.

A man has part of

\$4500

invested at

4\%

and the rest at

6\%.

If his annual return on each investment is the same, the average rate of interest which he realizes on the

\$4500

is:

5\%

4.8\%

5.2\%

4.6\%

none of these

Let

x

be the amount invested at

4\%

and equate the two returns

Solve

0.04x=0.06(4500-x)

, then find the total return

Let

x

dollars be invested at

4\%.

Equal returns give

0.04x=0.06(4500-x),

x=2700.

Each investment returns

\$108,

for a total of

\$216.

The average rate is

\frac{216}{4500}=0.048=4.8\%.

Thus, the correct answer is B.

Problem 17 in other years