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Mashcka [7]
1 year ago
11

Aliya deposited half as much money in a savings account earning 1.9% simple interest as she invested in a money market account t

hat earns 3.7% simple interest. If the total interest after one year is $297.60 , how much did she invest in each account?Ive tried this problem several times and I just think I don't know how to do it because every time I get the wrong answer.
Physics
1 answer:
yanalaym [24]1 year ago
3 0

Let <em>A</em> be the amount of money that Aliya deposited in the savings account. Since <em>A</em> is half as much as money as she invested in a money market account, then the amount that she invested in the market account is <em>2A.</em>

<em />

Express the interest that Aliya earned in terms of A. Set it equal to the amount of $297.60 and then solve for <em>A</em>.

Since the savings account gives 1.9% simple interest, the total amount of interest that she will earn from the savings account is 1.9% of A, which is equal to:

\frac{1.9}{100}\times A

Since the money market account gives 3.7% simple interest, the total amount of interest that she will earn from the money market account, is 3.7% of <em>2A</em>, which is equal to:

\frac{3.7}{100}\times2A

Add both interests in terms of A and simplify the expression:

\begin{gathered} \frac{1.9}{100}\times A+\frac{3.7}{100}\times2A \\ =\frac{1.9}{100}\times A+\frac{7.4}{100}\times A \\ =(\frac{1.9}{100}+\frac{7.4}{100})\times A \\ =\frac{1.9+7.4}{100}\times A \\ =\frac{9.3}{100}\times A \end{gathered}

The expression (9.3/100)*A represents the total interest after one year. Then:

\begin{gathered} \frac{9.3}{100}\times A=297.60 \\ \Rightarrow A=\frac{100}{9.3}\times297.60 \\ \Rightarrow A=\frac{100\times297.60}{9.3} \\ \Rightarrow A=\frac{29760}{9.3} \\ \Rightarrow A=3200 \end{gathered}

Use the value of <em>A</em> to find the amount that was invested in the money market account:

2A=2\times3200=6400

Therefore, Aliya deposited 3200 in a savings account and 6400 in a money market account.

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