Let's define the following variables to represent the amounts Ana invests in each of the three ways:

• Let $x$ be the amount Ana invests in the savings bonds (at 2.5% interest).
• Let $6x$ be the amount Ana invests in mutual funds (which is 6 times the amount she invests in the savings bonds, at 7% interest).
• Let $y$ be the amount Ana invests in the money market account (at 4.5% interest).

Ana has a total of $13,000 to invest. So, the first equation is:

$x + 6x + y = 13,000$ Simplifying this, we get: 7x + y = 13,000 \tag{1}

The interest (or return) Ana earns in the first year is $715. The interest from each investment is calculated as follows:

• The interest from the savings bonds is $0.025 \cdot x$.
• The interest from the mutual funds is $0.07 \cdot 6x$.
• The interest from the money market account is $0.045 \cdot y$.

The total interest earned is $715, so the second equation is:

$0.025x + 0.07(6x) + 0.045y = 715$ Simplifying the second equation: $0.025x + 0.42x + 0.045y = 715$ 0.445x + 0.045y = 715 \tag{2}

System of Equations

We now have the following system of linear equations:

1. $7x + y = 13,000$
2. $0.445x + 0.045y = 715$

These two equations can be solved to find the values of $x$ (investment in savings bonds), $6x$ (investment in mutual funds), and $y$ (investment in the money market account).

Would you like me to solve these equations for you?

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5 Related Questions:

1. How do you solve a system of linear equations using substitution?
2. How do you solve a system of linear equations using elimination?
3. What is the importance of setting up proper variables when solving real-life problems?
4. How does interest compounding differ from simple interest in investments?
5. How do you calculate the total return on investments over multiple years?

Tip: When dealing with investment problems, always ensure the total sum of all parts matches the original investment amount.