Question 1

Solve the problem.
-A bank loaned out $57,000, part of it at the rate of 2.5% per year and the rest at a rate of 3.5% per year. If the interest received was $1705.00, how much was loaned at 2.5%?

Accepted Answer

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

Question 2

Solve the problem.
-Your home state uses a linear model y= 48(x - 70) + 5750 to predict the number of vacationers (y) as compared to the average temperature for that week (x). Find the number of vacationers
Predicted for a week with an average temperature of 79 degrees.

Accepted Answer

Substituting x = 79 into the linear model gives y = 48(79 - 70) + 5750 = 48(9) + 5750 = 432 + 5750 = 6182 vacationers.

Question 3

Solve the problem.
-Roberto invested some money at 2.5%, and then invested $4000 more than twice this amount at 4%. His total annual income from the two investments was $1735.00. How much was invested at
4%?

Accepted Answer

The answer of Solve the problem.
-Roberto invested some money at...

Question 4

Solve the problem.
-Tom Quig traveled 270 miles east of St. Louis. For most of the trip he averaged 60 mph, but for one period of time he was slowed to 10 mph due to a major accident. If the total time of travel was 7
Hours, how many miles did he drive at the reduced speed?

Accepted Answer

Let $ x $ be the distance Tom drove at 10 mph. Then, the distance he drove at 60 mph is $ 270 - x $ miles. The time spent driving at 10 mph is $ \frac{x}{10} $ hours, and the time spent driving at 60 mph is $ \frac{270 - x}{60} $ hours. The total time is 7 hours, so we have the equation:$$ \frac{x}{10} + \frac{270 - x}{60} = 7 $$Multiplying every term by 60 to clear the denominators gives:$$ 6x + 270 - x = 420 $$Solving for $ x $ gives:$$ 5x = 150 $$$$ x = 30 $$Therefore, Tom drove 30 miles at the reduced speed.

Question 5

Solve the problem.
-Mardi received an inheritance of $60,000. She invested part at 1.25% and deposited the remainder in tax-free bonds at 2%. Her total annual income from the investments was $825. Find the amount
Invested at 1.25%.

Accepted Answer

Mardi invested $50,000 at 1.25% to earn $625 (1.25% of $50,000) and the remaining $10,000 at 2% to earn $200 (2% of $10,000), totaling $825 in annual income.

Question 6

Solve the problem.
-An airplane leaves Los Angeles for Denver at a speed of 420 mph. Thirty minutes later, a plane going from Denver to Los Angeles leaves Denver, which is 850 miles from Los Angeles, at a speed
Of 520 mph. When they meet, how far are they from Denver?

Accepted Answer

The first plane has a 30-minute head start, so it covers 420 mph * 0.5 hours = 210 miles before the second plane starts. The remaining distance when the second plane starts is 850 miles - 210 miles = 640 miles. The planes are closing in on each other at a combined speed of 420 mph + 520 mph = 940 mph. To cover the remaining 640 miles at 940 mph, it takes 640 miles / 940 mph = 0.68085 hours. In this time, the plane from Denver covers 520 mph * 0.68085 hours = 354 miles. Therefore, when they meet, they are 354 miles from Denver.

Question 7

Solve the problem.
-A computer company uses the linear model y = -22x + 50,787 to predict the decline in sales of a computer after it has been on the market more than one year. If x is the number of months after
The first year and y is the number of computers sold during that month, how many computers will
Be sold 15 months after the first year?

Accepted Answer

To find the number of computers sold 15 months after the first year, substitute x = 15 into the equation y = -22x + 50,787. This gives y = -22(15) + 50,787 = -330 + 50,787 = 50,457 computers.

Question 8

Solve the problem.
-A chemist needs 120 milliliters of a 40% solution but has only 30% and 54% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Accepted Answer

The answer of Solve the problem.
-A chemist needs 120 milliliters...

Question 9

Solve the problem.
-Walt made an extra $8000 last year from a part-time job. He invested part of the money at 3% and the rest at 3.25%. He made a total of $247.50 in interest. How much was invested at 3.25%?

Accepted Answer

Let the amount invested at 3.25% be x. Therefore, the amount invested at 3% is $8000 - x. The total interest from both investments is $247.50. The equation for the total interest is 0.0325x + 0.03(8000 - x) = 247.50. Solving this equation for x gives the amount invested at 3.25%, which is $3000.

Question 10

Solve the problem.
-An airplane flies from Metro City to Gotham with a tailwind that increases its normal speed by 100 mph. On the return trip, the plane must fly against this wind, which decreases its normal
Speed by the same amount. The flight from Metro City takes 3.71 hours and the return trip takes
8)67 hours. How far is it from Metro City to Gotham?

Accepted Answer

The answer of Solve the problem.
-An airplane flies from Metro...

Question 11

Solve the problem.
-Kevin invested part of his $5000 bonus in a certificate of deposit that paid 2% annual simple interest, and the remainder in a mutual fund that paid 4% annual simple interest. If his total
Interest for that year was $110, how much did Kevin invest in the mutual fund?

Accepted Answer

Let the amount invested in the certificate of deposit be $x. Therefore, the amount invested in the mutual fund is $5000 - x. The interest from the certificate of deposit is 0.02x, and the interest from the mutual fund is 0.04(5000 - x). The total interest is $110, so we have the equation 0.02x + 0.04(5000 - x) = 110. Solving this equation for x gives us the amount invested in the certificate of deposit, and subtracting this from $5000 gives the amount invested in the mutual fund, which is $500.

Question 12

Solve the problem.
-In a chemistry class, 7 liters of a 4% silver iodide solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?

Accepted Answer

Let x be the number of liters of the 10% solution needed.4% of 7 liters = 0.28 liters of silver iodide10% of x liters = 0.1x liters of silver iodideIn the final solution, 6% of (7 + x) liters = 0.06(7 + x) liters of silver iodideSince the amount of silver iodide is the same in all solutions, we can set up the equation:0.28 + 0.1x = 0.06(7 + x)0.28 + 0.1x = 0.42 + 0.06x0.04x = 0.14x = 3.5Therefore, 3.5 liters of the 10% solution are needed.

Question 13

Solve the problem.
-A toy company uses the linear model y = -2x + 597 to predict the decline in sales of a toy after it has been on the market more than one year. If x is the number of months after the first year and y
Is the number of toys sold in hundreds during that month, how many toys will be sold 9 months
After the first year?

Accepted Answer

Plugging x = 9 into the equation y = -2(9) + 597 gives y = -18 + 597 = 579. Since y represents hundreds of toys, 579 corresponds to 57,900 toys.

Question 14

Solve the problem.
-It is necessary to have a 40% antifreeze solution in the radiator of a certain car. The radiator now has 50 liters of 20% solution. How many liters of this should be drained and replaced with 100%
Antifreeze to get the desired strength?

Accepted Answer

To achieve a 40% antifreeze solution, we can use the equation of concentration: (initial volume * initial concentration + added volume * added concentration - drained volume * initial concentration) / final volume = desired concentration. Here, the added and drained volumes are the same, so we simplify to (initial volume * initial concentration + added volume * (100% - initial concentration)) / final volume = desired concentration. Substituting the given values (50 liters * 20% + added volume * 80%) / 50 liters = 40%, we find that the added (and thus drained) volume is 12.5 liters.

Question 15

Solve the problem.
-On a recent trip, Sarahʹs car traveled 20 mph faster on the first 150 miles than it did on the remaining 80 miles. The total time for the trip was 4 hr. Find the speed of Sarahʹs car on the first
Part of the trip.

Accepted Answer

The speed for the first part of the trip can be found by setting up an equation based on the given information. Let x be the speed (in mph) for the second part of the trip. Then, the speed for the first part of the trip is x + 20 mph. The time to cover the first 150 miles is 150/(x + 20) hours, and the time to cover the remaining 80 miles is 80/x hours. The total time for the trip is 4 hours, so the equation is 150/(x + 20) + 80/x = 4. Solving this equation for x gives the speed for the second part of the trip, and adding 20 to this speed gives the speed for the first part of the trip, which is 66 mph.

Question 16

Solve the problem.
-Helen Weller invested $11,000 in an account that pays 1.5% simple interest. How much additional money must be invested in an account that pays 3% simple interest so that the average return on
The two investments amounts to 2%?

Accepted Answer

The answer of Solve the problem.
-Helen Weller invested $11,000 in...

Question 17

Solve the problem.
-How many liters of a 30% alcohol solution must be mixed with 50 liters of a 70% solution to get a 40% solution?

Accepted Answer

To solve this, we can set up an equation based on the amount of alcohol in each solution. Let x be the amount of 30% alcohol solution needed. The total amount of alcohol from the 30% solution is 0.30x liters, and from the 70% solution, it's 0.70*50 liters. The final mixture will have (x + 50) liters of solution at 40% alcohol. Setting up the equation: 0.30x + 0.70*50 = 0.40(x + 50). Solving for x gives x = 150 liters.

Question 18

Solve the problem.
-A personʹs emotional quotient (EQ) is found by multiplying emotional age by 100 and dividing by chronological age. Using this information, if a 8 yr old person has an EQ of 92 what is that personʹs
Emotional age?

Accepted Answer

The EQ is calculated as (Emotional Age / Chronological Age) * 100 = EQ. Given an EQ of 92 for an 8-year-old, we solve for Emotional Age: (Emotional Age / 8) * 100 = 92. Simplifying, Emotional Age = 92 * 8 / 100 = 7.36 years old.

Question 19

Solve the problem.
-Don James wants to invest $55,000 to earn $1336 per year. He can invest in B-rated bonds paying 3.8% per year or in a Certificate of Deposit (CD) paying 1.2% per year. How much money should
Be invested in each to realize exactly $1336 in interest per year?

Accepted Answer

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

Question 20

Solve the problem.
-How much pure acid should be mixed with 3 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...

Quiz 1: Equations and Inequalities

Solve the problem. -A bank loaned out $57,000, part of it at the rate of 2.5% per year and the rest at a rate of 3.5% per year. If the interest received was $1705.00, how much was loaned at 2.5%?

Solve the problem. -Your home state uses a linear model y= 48(x - 70) + 5750 to predict the number of vacationers (y) as compared to the average temperature for that week (x) . Find the number of vacationers Predicted for a week with an average temperature of 79 degrees.

Solve the problem. -Roberto invested some money at 2.5%, and then invested $4000 more than twice this amount at 4%. His total annual income from the two investments was $1735.00. How much was invested at 4%?

Solve the problem. -Tom Quig traveled 270 miles east of St. Louis. For most of the trip he averaged 60 mph, but for one period of time he was slowed to 10 mph due to a major accident. If the total time of travel was 7 Hours, how many miles did he drive at the reduced speed?

Solve the problem. -Mardi received an inheritance of $60,000. She invested part at 1.25% and deposited the remainder in tax-free bonds at 2%. Her total annual income from the investments was $825. Find the amount Invested at 1.25%.

Solve the problem. -An airplane leaves Los Angeles for Denver at a speed of 420 mph. Thirty minutes later, a plane going from Denver to Los Angeles leaves Denver, which is 850 miles from Los Angeles, at a speed Of 520 mph. When they meet, how far are they from Denver?

Solve the problem. -A chemist needs 120 milliliters of a 40% solution but has only 30% and 54% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Solve the problem. -Walt made an extra $8000 last year from a part-time job. He invested part of the money at 3% and the rest at 3.25%. He made a total of $247.50 in interest. How much was invested at 3.25%?

Solve the problem. -Kevin invested part of his $5000 bonus in a certificate of deposit that paid 2% annual simple interest, and the remainder in a mutual fund that paid 4% annual simple interest. If his total Interest for that year was $110, how much did Kevin invest in the mutual fund?

Solve the problem. -In a chemistry class, 7 liters of a 4% silver iodide solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?

Solve the problem. -It is necessary to have a 40% antifreeze solution in the radiator of a certain car. The radiator now has 50 liters of 20% solution. How many liters of this should be drained and replaced with 100% Antifreeze to get the desired strength?

Solve the problem. -On a recent trip, Sarahʹs car traveled 20 mph faster on the first 150 miles than it did on the remaining 80 miles. The total time for the trip was 4 hr. Find the speed of Sarahʹs car on the first Part of the trip.

Solve the problem. -Helen Weller invested $11,000 in an account that pays 1.5% simple interest. How much additional money must be invested in an account that pays 3% simple interest so that the average return on The two investments amounts to 2%?

Solve the problem. -How many liters of a 30% alcohol solution must be mixed with 50 liters of a 70% solution to get a 40% solution?

Solve the problem. -A personʹs emotional quotient (EQ) is found by multiplying emotional age by 100 and dividing by chronological age. Using this information, if a 8 yr old person has an EQ of 92 what is that personʹs Emotional age?

Solve the problem. -Don James wants to invest $55,000 to earn $1336 per year. He can invest in B-rated bonds paying 3.8% per year or in a Certificate of Deposit (CD) paying 1.2% per year. How much money should Be invested in each to realize exactly $1336 in interest per year?

Solve the problem. -How much pure acid should be mixed with 3 gallons of a 50% acid solution in order to get an 80% acid solution?