Question

Murray’s father deposited $6,000 of his savings into two accounts. One account earns 1.5 percent interest, and the other account earns 2.5 percent interest. At the end the year, the interest in the account that earned 2.5 percent was $110.00 more than the other account. Which system represents the amounts of money, x and y, that was put into each account?
x + y = 6,000. 0.025 x + 0.015 y = 110.
x + y = 6,000. 0.25 x + 0.15 y = 110.
x + y = 6,000. 0.025 x minus 0.015 y = 110.
x + y = 6,000. 2.5 x minus 1.5 y = 110.

Answer 1

To solve the problem step by step, we designate:

- \( x \): the amount deposited in the account earning 2.5% interest.
- \( y \): the amount deposited in the account earning 1.5% interest.

We know that:

1. The total amount deposited is $6,000:
\[
x + y = 6000
\]

2. The interest earned from the account with 2.5% interest is $110 more than the interest earned from the account with 1.5% interest. The interest can be expressed as follows:
- Interest from the 2.5% account: \( 0.025x \)
- Interest from the 1.5% account: \( 0.015y \)

Thus, the equation for the interest difference can be expressed as:
\[
0.025x = 0.015y + 110
\]

This can also be rearranged to:
\[
0.025x - 0.015y = 110
\]

Now we can summarize the two equations:

1. \( x + y = 6000 \)
2. \( 0.025x - 0.015y = 110 \)

Now, let's compare this with the options provided:

1. **Option 1**: \( x + y = 6000 \) and \( 0.025x + 0.015y = 110 \) (Incorrect: the signs and coefficients don't match)
2. **Option 2**: \( x + y = 6000 \) and \( 0.25x + 0.15y = 110 \) (Incorrect: the coefficients are too high)
3. **Option 3**: \( x + y = 6000 \) and \( 0.025x - 0.015y = 110 \) (Correct)
4. **Option 4**: \( x + y = 6000 \) and \( 2.5x - 1.5y = 110 \) (Incorrect: the equation structure is not in line with our calculations)

The correct system of equations representing the amounts of money in each account is:

\[
\begin{cases}
x + y = 6000 \\
0.025x - 0.015y = 110
\end{cases}
\]

So **Option 3** is the correct choice.