방정식과 부등식 전체 문제

Hattie had $3,000 to invest and wants to earn 10.6% interest per year. She will put some of the money into an account that earns 12% per year and the rest into an account that earns 10% per year. How much money should she put into each account?

Carol invested $2,560 into two accounts. One account paid 8% interest and the other paid 6% interest. She earned 7.25% interest on the total investment. How much money did she put in each account?

Solve Interest Applications

In the following exercises, translate to a system of equations and solve.

Sam invested $48,000, some at 6% interest and the rest at 10%. How much did he invest at each rate if he received $4,000 in interest in one year?

Solve Interest Applications

In the following exercises, translate to a system of equations and solve.

Arnold invested $64,000, some at 5.5% interest and the rest at 9%. How much did he invest at each rate if he received $4,500 in interest in one year?

After four years in college, Josie owes $65,800 in student loans. The interest rate on the federal loans is 4.5% and the rate on the private bank loans is 2%. The total interest she owed for one year was $2,878.50. What is the amount of each loan?

Mark wants to invest $10,000 to pay for his daughter’s wedding next year. He will invest some of the money in a short term CD that pays 12% interest and the rest in a money market savings account that pays 5% interest. How much should he invest at each rate if he wants to earn $1,095 in interest in one year?

A trust fund worth $25,000 is invested in two different portfolios. This year, one portfolio is expected to earn 5.25% interest and the other is expected to earn 4%. Plans are for the total interest on the fund to be $1150 in one year. How much money should be invested at each rate?

A business has two loans totaling $85,000. One loan has a rate of 6% and the other has a rate of 4.5%. This year, the business expects to pay $4650 in interest on the two loans. How much is each loan?

Laurie was completing the treasurer’s report for her son’s Boy Scout troop at the end of the school year. She didn’t remember how many boys had paid the $15 full-year registration fee and how many had paid the $10 partial-year fee. She knew that the number of boys who paid for a full-year was ten more than the number who paid for a partial-year. If $250 was collected for all the registrations, how many boys had paid the full-year fee and how many had paid the partial-year fee?

As the treasurer of her daughter’s Girl Scout troop, Laney collected money for some girls and adults to go to a three-day camp. Each girl paid $75 and each adult paid $30. The total amount of money collected for camp was $765. If the number of girls is three times the number of adults, how many girls and how many adults paid for camp?

Take a handful of two types of coins, and write a problem similar to (see text) relating the total number of coins and their total value. Set up a system of equations to describe your situation and then solve it.

In (see text) we solved the system of equations $\left\{\begin{array}{l}b+f=21,540 \\ 0.105b+0.059f=1669.68\end{array}\right.$ by substitution. Would you have used substitution or elimination to solve this system? Why?

Determine Whether an Ordered Pair is a Solution of a System of Equations.

In the following exercises, determine if the following points are solutions to the given system of equations.

$\left\{\begin{array}{l}x+3y=-9 \\ 2x-4y=12\end{array}\right.$

ⓐ $(-3,-2)$ ⓑ $(0,-3)$

Determine Whether an Ordered Pair is a Solution of a System of Equations.

In the following exercises, determine if the following points are solutions to the given system of equations.

$\left\{\begin{array}{l}x+y=8 \\ y=x-4\end{array}\right.$

ⓐ $(6,2)$ ⓑ $(9,-1)$

Solve a System of Linear Equations by Graphing

In the following exercises, solve the following systems of equations by graphing.

$\left\{\begin{array}{l}3x+y=6 \\ x+3y=-6\end{array}\right.$

Solve a System of Linear Equations by Graphing

In the following exercises, solve the following systems of equations by graphing.

$\left\{\begin{array}{l}y=x-2 \\ y=-2x-2\end{array}\right.$

Solve a System of Linear Equations by Graphing

In the following exercises, solve the following systems of equations by graphing.

$\left\{\begin{array}{l}2x-y=6 \\ y=4\end{array}\right.$

Solve a System of Linear Equations by Graphing

In the following exercises, solve the following systems of equations by graphing.

$\left\{\begin{array}{l}x+4y=-1 \\ x=3\end{array}\right.$

Solve a System of Linear Equations by Graphing

In the following exercises, solve the following systems of equations by graphing.

$\left\{\begin{array}{l}2x-y=5 \\ 4x-2y=10\end{array}\right.$

Solve a System of Linear Equations by Graphing

In the following exercises, solve the following systems of equations by graphing.

$\left\{\begin{array}{l}-x+2y=4 \\ y=\frac{1}{2}x-3\end{array}\right.$