Juan invests 225,000 in two accounts. He would like to earn...

Juan invests $\$ 225,000$ in two accounts. He would like to earn $\$ 7900$ a year to pay some expenses. Juan invests part of the money in an account paying $3 \%$ simple interest and the rest in an account paying $4 \%$ simple interest. a. Write a system of equations that will help Juan find the amount that should be invested in each account. b. How much does Juan need to invest in each account to earn $\$ 7900$ per year?

Juan invests $\$ 225,000$ in two accounts. He would like to earn $\$ 7900$ a year to pay some expenses. Juan invests part of the money in an account paying $3 \%$ simple interest and the rest in an account paying $4 \%$ simple interest.
a. Write a system of equations that will help Juan find the amount that should be invested in each account.
b. How much does Juan need to invest in each account to earn $\$ 7900$ per year?

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Key Concepts

Simple Interest

Simple interest is a method for calculating the interest charge on a principal sum where interest is computed only on the original amount invested or borrowed, rather than on a reinvested interest amount. This concept is often used in basic finance problems to determine earnings or costs over time based on a fixed rate.

System of Equations

A system of equations involves two or more equations with multiple variables that are solved together because the variables are interdependent. This concept is key to solving problems where several conditions or constraints need to be met simultaneously, such as splitting an investment among different options.

Mixture Problems

Mixture problems are a type of word problem in which two or more entities with different characteristics are combined, and the goal is to determine the amounts of each component. In the context of financial investments, this often involves allocating a total sum of money across different interest rates to achieve a desired overall return.

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