# 5.5 Solve mixture applications with systems of equations  (Page 4/7)

 Page 4 / 7

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.

## Solve interest applications

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? ## Solution  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? ## Solution  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.

Amara currently sells televisions for company A at a salary of $17,000 plus a$100 commission for each television she sells. Company B offers her a position with a salary of $29,000 plus a$20 commission for each television she sells. How many televisions would Amara need to sell for the options to be equal?
what is the quantity and price of the televisions for both options?
karl
I'm mathematics teacher from highly recognized university.
is anyone else having issues with the links not doing anything?
Yes
Val
chapter 1 foundations 1.2 exercises variables and algebraic symbols
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Joseph would like to make 12 pounds of a coffee blend at a cost of $6.25 per pound. He blends Ground Chicory at$4.40 a pound with Jamaican Blue Mountain at $8.84 per pound. How much of each type of coffee should he use? Samer 4x6.25=$25 coffee blend 4×4.40= $17.60 ground chicory 4x8.84= 35.36 blue mountain. In total they will spend for 12 pounds$77.96 they will spend in total
tyler
DaMarcus and Fabian live 23 miles apart and play soccer at a park between their homes. DaMarcus rode his bike for three-quarters of an hour and Fabian rode his bike for half an hour to get to the park. Fabian’s speed was six miles per hour faster than DaMarcus’ speed. Find the speed of both soccer players.
i need help how to do this is confusing
what kind of math is it?
Danteii
help me to understand
huh, what is the algebra problem
Daniel
How many soldiers are there in a group of 27 sailors and soldiers if there are four fifths many sailors as soldiers?
tyler
What is the domain and range of heaviside
What is the domain and range of Heaviside and signum
Christopher
25-35
Fazal
The hypotenuse of a right triangle is 10cm long. One of the triangle’s legs is three times the length of the other leg. Find the lengths of the three sides of the triangle.
Tickets for a show are $70 for adults and$50 for children. For one evening performance, a total of 300 tickets were sold and the receipts totaled \$17,200. How many adult tickets and how many child tickets were sold?
A 50% antifreeze solution is to be mixed with a 90% antifreeze solution to get 200 liters of a 80% solution. How many liters of the 50% solution and how many liters of the 90% solution will be used?
June needs 45 gallons of punch for a party and has 2 different coolers to carry it in. The bigger cooler is 5 times as large as the smaller cooler. How many gallons can each cooler hold?
Washing his dad’s car alone, eight-year-old Levi takes 2.5 hours. If his dad helps him, then it takes 1 hour. How long does it take the Levi’s dad to wash the car by himself?
Bruce drives his car for his job. The equation R=0.575m+42 models the relation between the amount in dollars, R, that he is reimbursed and the number of miles, m, he drives in one day. Find the amount Bruce is reimbursed on a day when he drives 220 miles.