Question 1

Solve the problem.
-Don James wants to invest $69,000 to earn $4210 per year. He can invest in B-rated bonds paying 9% per year or in a Certificate of Deposit (CD) paying 4% per year. How much money should be invested in each to realize
Exactly $4210 in interest per year?

Accepted Answer

The answer of Solve the problem.
-Don James wants to invest...

Question 2

Solve the problem.
-How can $28,000 be invested, part at 4% annual interest and the remainder at 10% annual interest, so that the interest earned by the two accounts is equal at the end of the year?

Accepted Answer

The answer of Solve the problem.
-How can $28,000 be invested,...

Question 3

Solve the problem.
-Melissa invested a sum of money at 3% annual interest. She invested three times that sum at 5% annual interest. If her total yearly interest from both investments was $5400, how much was invested at 3%?

Accepted Answer

Let x be the amount invested at 3%. Then 3x is invested at 5%. The equation for total interest is 0.03x + 0.05(3x) = 5400. Solving this gives x = $30,000.

Question 4

Solve the problem.
-Kevin invested part of his $10,000 bonus in a certificate of deposit that paid 6% annual interest, and the remainder in a mutual fund that paid 11% annual interest. If his total interest for that year was $800, how much
Did Kevin invest in the mutual fund?

Accepted Answer

Let x be the amount invested in the mutual fund. Then, $10,000 - x is the amount invested in the certificate of deposit. The equation for total interest is 0.06(10,000 - x) + 0.11x = 800. Solving this equation gives x = $4000.

Question 5

Solve the problem.
-A vendor sells hot dogs and bags of potato chips. A customer buys 2 hot dogs and 3 bags of potato chips for $6.25. Another customer buys 3 hot dogs and 5 bags of potato chips for $9.75. Find the cost of each item.

Accepted Answer

The answer of Solve the problem.
-A vendor sells hot dogs...

Question 6

Solve the problem.
-Sue took her collection of nickels and dimes to deposit in the bank. She has five fewer nickels than dimes. Her total deposit was $64.85. How many dimes did she deposit?

Accepted Answer

Let the number of dimes be $d$ and the number of nickels be $n$. The problem states that Sue has five fewer nickels than dimes, so $n = d - 5$. The total value of the coins is $64.85, or 6485 cents. Since dimes are worth 10 cents and nickels are worth 5 cents, the equation for the total value is $10d + 5n = 6485$. Substituting $n = d - 5$ into the equation gives $10d + 5(d - 5) = 6485$. Simplifying, $10d + 5d - 25 = 6485$, so $15d = 6510$, and dividing by 15 gives $d = 434$. Therefore, Sue deposited 434 dimes.

Question 7

Solve the problem.
-How much pure acid should be mixed with 4 gallons of a 50% acid solution in order to get an 80% acid solution?

Accepted Answer

The answer of Solve the problem.
-How much pure acid should...

Question 8

Solve the problem.
-The owners of a candy store want to sell, for $6 per pound, a mixture of chocolate-covered raisins, which usually sells for $3 per pound, and chocolate-covered macadamia nuts, which usually sells for $8 per pound.
They have a 30-pound barrel of the raisins. How many pounds of the nuts should they mix with the barrel of
Raisins so that they hit their target value of $6 per pound for the mixture?

Accepted Answer

The answer of Solve the problem.
-The owners of a candy...

Question 9

Solve the problem.
-The manager of a candy shop sells chocolate covered peanuts for $5 per pound and chocolate covered cashews for $15 per pound. The manager wishes to mix 30 pounds of the cashews to get a cashew-peanut mixture that
Will sell for $11 per pound. How many pounds of peanuts should be used?

Accepted Answer

The answer of Solve the problem.
-The manager of a candy...

Question 10

Solve the problem.
-The manager of a coffee shop has one type of coffee that sells for $6 per pound and another type that sells for $14 per pound. The manager wishes to mix 90 pounds of the $14 coffee to get a mixture that will sell for $11 per
Pound. How many pounds of the $6 coffee should be used?

Accepted Answer

The answer of Solve the problem.
-The manager of a coffee...

Question 11

Solve the problem.
-A chemist needs 12 liters of a 50% salt solution. All she has available is a 20% salt solution and a 70% salt solution. How much of each of the two solutions should she mix to obtain her desired solution?

Accepted Answer

To find the correct amounts, set up the equation: 0.2x + 0.7(12-x) = 0.5(12). Solving gives x = 4.8 liters of the 20% solution and 12 - x = 7.2 liters of the 70% solution.

Question 12

Solve the problem.
-A retired couple has $160,000 to invest to obtain annual income. They want some of it invested in safe Certificates of Deposit yielding 6%. The rest they want to invest in AA bonds yielding 11% per year. How much
Should they invest in each to realize exactly $15,600 per year?

Accepted Answer

Let x be the amount invested in AA bonds at 11%, and y be the amount invested in CDs at 6%. The total investment is $160,000, so x + y = $160,000. They want to earn $15,600 annually, so 0.11x + 0.06y = $15,600. Solving these equations simultaneously gives x = $120,000 and y = $40,000.

Question 13

Solve the problem.
-Jarod is having a problem with rabbits getting into his vegetable garden, so he decides to fence it in. The length of the garden is 9 feet more than 3 times the width. He needs 50 feet of fencing to do the job. Find the length and
Width of the garden.

Accepted Answer

The answer of Solve the problem.
-Jarod is having a problem...

Question 14

Solve the problem.
-A loan officer at a bank has $88,000 to lend and is required to obtain an average return of 8% per year. If he can lend at the rate of 9% or the rate of 7%, how much can he lend at the 7% rate and still meet his required return?

Accepted Answer

To find how much can be lent at 7%, let x be the amount lent at 7%. Then, the amount lent at 9% is $88,000 - x. The equation for the average return is: 0.07x + 0.09(88,000 - x) = 0.08(88,000). Solving this equation gives x = $44,000.

Question 15

Solve the problem.
-The radiator in a certain make of car needs to contain 40 liters of 40% antifreeze. The radiator now contains 40 liters of 20% antifreeze. How many liters of this solution must be drained and replaced with 100% antifreeze
To get the desired strength?

Accepted Answer

To achieve a 40% antifreeze solution in a 40-liter mixture, you need 40 * 0.4 = 16 liters of pure antifreeze. The current mixture has 40 * 0.2 = 8 liters of antifreeze. To increase the antifreeze content from 8 liters to 16 liters, you need to add 16 - 8 = 8 liters of pure antifreeze. If you remove x liters of the current mixture, you also remove 0.2x liters of antifreeze. To keep the total volume at 40 liters, you replace x liters of the mixture with x liters of pure antifreeze, which adds x liters of antifreeze. The equation to solve is 8 - 0.2x + x = 16, simplifying to 0.8x = 8, giving x = 10.

Question 16

Solve the problem.
-Jimmy is a partner in an Internet-based coffee supplier.The company offers gourmet coffee beans for $14 per pound and regular coffee beans for $6 per pound. Jimmy is creating a medium-price product that will sell for
$8 per pound.The first thing to go into the mixing bin was 10 pounds of the gourmet beans. How many pounds
Of the less expensive regular beans should be added?

Accepted Answer

To solve this, we use the concept of weighted averages. The goal is to find a mix that averages out to $8 per pound. Let $ x $ be the pounds of regular beans needed. The equation is $\frac{10 \times 14 + x \times 6}{10 + x} = 8$. Solving for $ x $ gives $ x = 30 $ pounds.

Question 17

Solve the problem.
-A college student earned $7000 during summer vacation working as a waiter in a popular restaurant. The student invested part of the money at 10% and the rest at 9%. If the student received a total of $656 in interest at
The end of the year, how much was invested at 10%?

Accepted Answer

The answer of Solve the problem.
-A college student earned $7000...

Question 18

Solve the problem.
-If $2000 is invested at 10% annual interest, how much should be invested at 12% annual interest so that the total yearly income from both investments is $5000?

Accepted Answer

To find the amount to be invested at 12%, let x be the amount. The income from $2000 at 10% is $200. The income from x at 12% is 0.12x. The total income is $200 + 0.12x = $5000. Solving for x gives x = $40,000.

Question 19

Solve the problem.
-The three angles in a triangle always add up to 180°. If one angle in a triangle is 56° and the second is 3 times the third, what are the three angles?

Accepted Answer

The third angle is x, so the second angle is 3x. The equation is 56 + 3x + x = 180. Solving gives x = 31, so the angles are 56°, 93°, and 31°.

Question 20

Solve the problem.
-A bank loaned out $57,000, part of it at the rate of 11% per year and the rest at a rate of 7% per year. If the interest received was $4990, how much was loaned at 11%?

Accepted Answer

The answer of Solve the problem.
-A bank loaned out $57,000,...

Quiz 4: Systems of Linear Equations

Solve the problem. -Don James wants to invest $69,000 to earn $4210 per year. He can invest in B-rated bonds paying 9% per year or in a Certificate of Deposit (CD) paying 4% per year. How much money should be invested in each to realize Exactly $4210 in interest per year?

Solve the problem. -How can $28,000 be invested, part at 4% annual interest and the remainder at 10% annual interest, so that the interest earned by the two accounts is equal at the end of the year?

Solve the problem. -Melissa invested a sum of money at 3% annual interest. She invested three times that sum at 5% annual interest. If her total yearly interest from both investments was $5400, how much was invested at 3%?

Solve the problem. -Kevin invested part of his $10,000 bonus in a certificate of deposit that paid 6% annual interest, and the remainder in a mutual fund that paid 11% annual interest. If his total interest for that year was $800, how much Did Kevin invest in the mutual fund?

Solve the problem. -A vendor sells hot dogs and bags of potato chips. A customer buys 2 hot dogs and 3 bags of potato chips for $6.25. Another customer buys 3 hot dogs and 5 bags of potato chips for $9.75. Find the cost of each item.

Solve the problem. -Sue took her collection of nickels and dimes to deposit in the bank. She has five fewer nickels than dimes. Her total deposit was $64.85. How many dimes did she deposit?

Solve the problem. -How much pure acid should be mixed with 4 gallons of a 50% acid solution in order to get an 80% acid solution?

Solve the problem. -A chemist needs 12 liters of a 50% salt solution. All she has available is a 20% salt solution and a 70% salt solution. How much of each of the two solutions should she mix to obtain her desired solution?

Solve the problem. -A retired couple has $160,000 to invest to obtain annual income. They want some of it invested in safe Certificates of Deposit yielding 6%. The rest they want to invest in AA bonds yielding 11% per year. How much Should they invest in each to realize exactly $15,600 per year?

Solve the problem. -Jarod is having a problem with rabbits getting into his vegetable garden, so he decides to fence it in. The length of the garden is 9 feet more than 3 times the width. He needs 50 feet of fencing to do the job. Find the length and Width of the garden.

Solve the problem. -A loan officer at a bank has $88,000 to lend and is required to obtain an average return of 8% per year. If he can lend at the rate of 9% or the rate of 7%, how much can he lend at the 7% rate and still meet his required return?

Solve the problem. -The radiator in a certain make of car needs to contain 40 liters of 40% antifreeze. The radiator now contains 40 liters of 20% antifreeze. How many liters of this solution must be drained and replaced with 100% antifreeze To get the desired strength?

Solve the problem. -A college student earned $7000 during summer vacation working as a waiter in a popular restaurant. The student invested part of the money at 10% and the rest at 9%. If the student received a total of $656 in interest at The end of the year, how much was invested at 10%?

Solve the problem. -If $2000 is invested at 10% annual interest, how much should be invested at 12% annual interest so that the total yearly income from both investments is $5000?

Solve the problem. -The three angles in a triangle always add up to 180°. If one angle in a triangle is 56° and the second is 3 times the third, what are the three angles?

Solve the problem. -A bank loaned out $57,000, part of it at the rate of 11% per year and the rest at a rate of 7% per year. If the interest received was $4990, how much was loaned at 11%?