<< Chapter < Page  Chapter >> Page > 
Translate to a system of equations and solve:
Anatole needs to make 250 milliliters of a 25% solution of hydrochloric acid for a lab experiment. The lab only has a 10% solution and a 40% solution in the storeroom. How much of the 10% and how much of the 40% solutions should he mix to make the 25% solution?
Anatole should mix 125 ml of the 10% solution and 125 ml of the 40% solution.
The formula to model interest applications is I = Prt . Interest, I , is the product of the principal, P , the rate, r , and the time, t . In our work here, we will calculate the interest earned in one year, so t will be 1.
We modify the column titles in the mixture table to show the formula for interest, as you’ll see in [link] .
Translate to a system of equations and solve:
Adnan has $40,000 to invest and hopes to earn 7.1% interest per year. He will put some of the money into a stock fund that earns 8% per year and the rest into bonds that earns 3% per year. How much money should he put into each fund?
Step 1. Read the problem.  A chart will help us organize the information. 
Step 2. Identify what we are looking for.  We are looking for the amount to invest in each fund. 
Step 3. Name what we are looking for.  Let
$s=$ the amount invested in stocks.
$\phantom{\rule{1.5em}{0ex}}b=$ the amount invested in bonds. 
Write the interest rate as a decimal for
each fund. Multiply: Principal · Rate · Time to get the Interest. 

Step 4. Translate into a system of
equations. We get our system of equations from the Principal column and the Interest column. 

Step 5. Solve the system of equations
Solve by elimination. Multiply the top equation by −0.03. 

Simplify and add to solve for s .  
To find b , substitute s = 32,800 into the first equation. 

Step 6. Check the answer in the problem.  We leave the check to you. 
Step 7. Answer the question.  Adnan should invest $32,000 in stock and
$7,200 in bonds. 
Did you notice that the Principal column represents the total amount of money invested while the Interest column represents only the interest earned? Likewise, the first equation in our system, s + b = 40,000, represents the total amount of money invested and the second equation, 0.08 s + 0.03 b = 0.071(40,000), represents the interest earned.
Translate to a system of equations and solve:
Leon had $50,000 to invest and hopes to earn 6.2 % interest per year. He will put some of the money into a stock fund that earns 7% per year and the rest in to a savings account that earns 2% per year. How much money should he put into each fund?
Leon should put $42,000 in the stock fund and $8000 in the savings account.
Translate to a system of equations and solve:
Julius invested $7,000 into two stock investments. One stock paid 11% interest and the other stock paid 13% interest. He earned 12.5% interest on the total investment. How much money did he put in each stock?
Julius invested $1,750 at 11% and $5,250 at 13%.
Translate to a system of equations and solve:
Rosie owes $21,540 on her two student loans. The interest rate on her bank loan is 10.5% and the interest rate on the federal loan is 5.9%. The total amount of interest she paid last year was $1,669.68. What was the principal for each loan?
Step 1. Read the problem.  A chart will help us organize the information. 
Step 2. Identify what we are looking for.  We are looking for the principal of each loan. 
Step 3. Name what we are looking for.  Let
$b=$ the principal for the bank loan.
$\phantom{\rule{1.5em}{0ex}}f=$ the principal on the federal loan 
The total loans are $21,540.  
Record the interest rates as decimals
in the chart. 

Multiply using the formula
l = Pr
t to
get the Interest. 

Step 4. Translate into a system of
equations. The system of equations comes from the Principal column and the Interest column. 

Step 5. Solve the system of equations
We will use substitution to solve. Solve the first equation for b . 

Substitute
b = −
f + 21,540 into the
second equation. 

Simplify and solve for f .  
To find
b , substitute
f = 12,870 into
the first equation. 

Step 6. Check the answer in the
problem. 
We leave the check to you. 
Step 7. Answer the question.  The principal of the bank loan is $12,870 and
the principal for the federal loan is $8,670. 
Notification Switch
Would you like to follow the 'Elementary algebra' conversation and receive update notifications?