Question 1

Solve.
-When Milo got promoted at work, he received a 25% pay raise. He now earns $60,000 per year. What was his annual salary before his raise?
A)$48,000
B)$15,000
C)$60,000
D)$12,000

Accepted Answer

Milo's current salary is after a 25% increase, so he now earns 125% of his original salary. To find his original salary, divide his current salary by 1.25 (or 125%). $60,000 / 1.25 = $48,000.

Question 2

Solve.
-A college student earned $5200 during summer vacation working as a waiter in a popular restaurant. The student invested part of the money at 10% and the rest at 7%. If the student received a total of $445 in interest at
The end of the year, how much was invested at 10%?
A)$2700
B)$742
C)$2500
D)$2600

Accepted Answer

The total interest earned from both investments is $445. Let x be the amount invested at 10%, so the amount invested at 7% is $5200 - x. The interest from the first investment is 0.10x, and from the second investment is 0.07(5200 - x). The total interest is the sum of these, so 0.10x + 0.07(5200 - x) = 445. Solving this equation for x gives x = $2700, which is the amount invested at 10%.

Question 3

Solve.
-Libby's 4 quiz scores in her math class are 86, 91, 81, and 86. What score does she need to obtain on her next quiz to average an 85? Round to the nearest whole number if necessary.
A)84
B)82
C)67
D)81

Accepted Answer

To find the score needed on the next quiz to average 85, calculate the total score needed for 5 quizzes: 85 * 5 = 425. The sum of the current scores is 86 + 91 + 81 + 86 = 344. The score needed on the next quiz is 425 - 344 = 81.

Question 4

Solve.
-Amy charges $140 plus $35 an hour to do a friend's taxes. If her friend's total bill was $350, how many hours did Amy spend doing the taxes?
A)4 hours
B)14 hours
C)6 hours
D)350 hours

Accepted Answer

The answer of Solve.
-Amy charges $140 plus $35 an hour...

Question 5

Solve.
-A consultant charges $100 plus $25 an hour. How many hours did the consultant work if the total bill were $475?
A)15 hours
B)4 hours
C)19 hours
D)375 hours

Accepted Answer

The consultant charges $100 as a base fee and $25 per hour. To find the number of hours worked, subtract the base fee from the total bill: $475 - $100 = $375. Then divide by the hourly rate: $375 / $25 = 15 hours.

Question 6

Solve.
-The number of employees that work at a company has increased by 40% over the past year. This year there are 356 more employees with the company than last year. How many employees were there last year?
A)890 employees
B)14,240 employees
C)534 employees
D)8)9 employees

Accepted Answer

The increase of 356 employees represents a 40% growth from last year. To find the original number of employees, divide the increase by the growth rate: 356 / 0.40 = 890 employees last year.

Question 7

Solve.
-Alice invested some money at 19% simple interest. At the end of the year the total amount of her original principal and the interest was $11,305. How much did she originally invest?
A)$214,795
B)$1805
C)$9500
D)$595

Accepted Answer

The formula for simple interest is $I = P \times r \times t$, where $I$ is the interest earned, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. Here, we know the total amount after 1 year is $11,305, which includes the original principal plus the interest earned at a rate of 19% (or 0.19 in decimal form). Let $P$ be the original investment. The interest earned can be expressed as $P \times 0.19$. The total amount after 1 year is the sum of the original investment and the interest earned, so $P + P \times 0.19 = 11,305$. Simplifying, we get $1.19P = 11,305$, and solving for $P$ gives $P = 11,305 / 1.19 = 9500$.

Question 8

Solve.
-Kevin invested part of his $10,000 bonus in a certificate of deposit that paid 6% annual simple interest, and the remainder in a mutual fund that paid 11% annual simple interest. If his total interest for that year was $700,
How much did Kevin invest in the mutual fund?
A)$8000
B)$3000
C)$1000
D)$2000

Accepted Answer

Kevin invested $x in the certificate of deposit and $10,000 - x in the mutual fund. The equation for total interest is 0.06x + 0.11(10,000 - x) = 700. Solving for x gives $8,000 in the certificate of deposit, so $2,000 was invested in the mutual fund.

Question 9

Solve.
-Susan charges $250 plus $50 an hour to clean houses. If a client's total bill were $700, how many hours did Susan spend cleaning the client's house?
A)9 hours
B)450 hours
C)5 hours
D)14 hours

Accepted Answer

The total bill is $700, and Susan charges a flat rate of $250 plus $50 per hour. Subtracting the flat rate from the total gives $700 - $250 = $450. Dividing this by the hourly rate of $50 gives $450 / $50 = 9 hours.

Question 10

Solve.
-Allan's 4 quiz scores in his math class are 87, 89, 88, and 78. What score does he need to obtain on his exam to average an 85 if an exam counts as much as two quizzes?
A)68
B)76
C)83
D)84

Accepted Answer

The total number of quizzes and exams is 4 + 1 = 5. The total score needed is 85 * 5 = 425. The total score from the quizzes is 87 + 89 + 88 + 78 = 342. The score needed on the exam is 425 - 342 = 83.

Question 11

Solve.
-A bank loaned out $61,000, part of it at the rate of 11% per year and the rest at a rate of 5% per year. If the interest received was $4670, how much was loaned at 11%?
A)$34,000
B)$28,000
C)$27,000
D)$33,000

Accepted Answer

The answer of Solve.
-A bank loaned out $61,000, part of...

Question 12

Solve.
-Raymond's job pays $20 per hour for the first forty hours and $30 per hour for each hour in the week worked above the 40 hours. If he earned $980 this week, how many overtime hours did he work?
A)46 hours
B)6 hours
C)9 hours
D)180 hours

Accepted Answer

Raymond earns $20 per hour for the first 40 hours, totaling $800 (20*40). The remaining $180 (980-800) must come from overtime pay at $30 per hour. Dividing $180 by $30 gives 6 hours of overtime.

Question 13

Solve.
-Bruce and Elaine hired a magician for their daughter's birthday party. The magician charged $32 plus $4 for each child attending the party. The total bill came to $92. How many children attended the party?
A)23 children
B)60 children
C)8 children
D)15 children

Accepted Answer

The equation for the total cost is 32 + 4x = 92, where x is the number of children. Solving for x gives x = 15.

Question 14

Solve.
-A local animal shelter accepts abandoned cats and dogs. They usually receive three times as many cats as dogs. They estimate that 80% of the cats and 50% of the dogs that come in need some kind of medical treatment. If
They treated 319 animals last year, how many cats and dogs did they take in?
A)110 dogs, 113 cats
B)330 dogs, 990 cats
C)110 dogs, 330 cats
D)330 dogs, 110 cats

Accepted Answer

Let the number of dogs be $d$ and the number of cats be $c$. Given that $c = 3d$ and $0.8c + 0.5d = 319$. Solving these equations, we find $d = 110$ and $c = 330$.

Question 15

Solve.
-A salesperson in an expensive clothing store earns $2600 per month base pay plus a 6.5% commission on sales. One month she earns $5518.50. What were her sales for that month?
A)$294,450
B)$297,050
C)$44,900
D)$56,134

Accepted Answer

Her total earnings were $5518.50, which includes her base pay of $2600. Subtracting the base pay from her total earnings gives $5518.50 - $2600 = $2918.50, which is the amount she earned from commission. To find her sales, divide the commission amount by the commission rate: $2918.50 / 0.065 = $44,900.

Question 16

Solve.
-A brother and sister split the $922,500 from the sale of their parent's house. According to the will, the sister was to receive 25% more than her brother, for having managed the property. How much money did the sister
Receive?
A)$512,500
B)$3,690,000
C)$230,625
D)$410,000

Accepted Answer

The total amount is $922,500. Let the brother's share be x. The sister's share is x + 25% of x = 1.25x. Together, their shares make up the total amount: x + 1.25x = 2.25x = $922,500. Solving for x gives x = $922,500 / 2.25 = $410,000 (brother's share). The sister's share is 1.25x = 1.25 * $410,000 = $512,500.

Question 17

Solve.
-Logan bought stocks and later sold them for $1,081,600, making a profit of 4%. How much did he pay for the stocks?
A)$1,040,000
B)$43,264
C)$41,600
D)$2.704e+09

Accepted Answer

The answer of Solve.
-Logan bought stocks and later sold them...

Question 18

Solve.
-Ming got a 19% raise in her salary from last year. This year she is earning $135,660. How much did she make last year?
A)$21,660
B)$114,000
C)$7140
D)$2,577,540

Accepted Answer

The answer of Solve.
-Ming got a 19% raise in her...

Question 19

Solve.
-Holly bought a sweater on sale for 20% off the original price. If she saved $12, what was the original price?
A)$2.40
B)$60.00
C)$240.00
D)$48.00

Accepted Answer

The answer of Solve.
-Holly bought a sweater on sale for...

Question 20

Solve.
-Michael hired Heather to iron his dress shirts. Heather charges $40 an hour plus $0.25 for each shirt ironed. Heather worked 4 hours and sent a bill to Michael for $174. How many shirts did Heather iron?
A)224 shirts
B)696 shirts
C)14 shirts
D)56 shirts

Accepted Answer

The answer of Solve.
-Michael hired Heather to iron his dress...

Quiz 2: Equations, Inequalities, and Applications

Solve. -When Milo got promoted at work, he received a 25% pay raise. He now earns $60,000 per year. What was his annual salary before his raise?

Solve. -A college student earned $5200 during summer vacation working as a waiter in a popular restaurant. The student invested part of the money at 10% and the rest at 7%. If the student received a total of $445 in interest at The end of the year, how much was invested at 10%?

Solve. -Libby's 4 quiz scores in her math class are 86, 91, 81, and 86. What score does she need to obtain on her next quiz to average an 85? Round to the nearest whole number if necessary.

Solve. -Amy charges $140 plus $35 an hour to do a friend's taxes. If her friend's total bill was $350, how many hours did Amy spend doing the taxes?

Solve. -A consultant charges $100 plus $25 an hour. How many hours did the consultant work if the total bill were $475?

Solve. -The number of employees that work at a company has increased by 40% over the past year. This year there are 356 more employees with the company than last year. How many employees were there last year?

Solve. -Alice invested some money at 19% simple interest. At the end of the year the total amount of her original principal and the interest was $11,305. How much did she originally invest?

Solve. -Kevin invested part of his $10,000 bonus in a certificate of deposit that paid 6% annual simple interest, and the remainder in a mutual fund that paid 11% annual simple interest. If his total interest for that year was $700, How much did Kevin invest in the mutual fund?

Solve. -Susan charges $250 plus $50 an hour to clean houses. If a client's total bill were $700, how many hours did Susan spend cleaning the client's house?

Solve. -Allan's 4 quiz scores in his math class are 87, 89, 88, and 78. What score does he need to obtain on his exam to average an 85 if an exam counts as much as two quizzes?

Solve. -A bank loaned out $61,000, part of it at the rate of 11% per year and the rest at a rate of 5% per year. If the interest received was $4670, how much was loaned at 11%?

Solve. -Raymond's job pays $20 per hour for the first forty hours and $30 per hour for each hour in the week worked above the 40 hours. If he earned $980 this week, how many overtime hours did he work?

Solve. -Bruce and Elaine hired a magician for their daughter's birthday party. The magician charged $32 plus $4 for each child attending the party. The total bill came to $92. How many children attended the party?

Solve. -A salesperson in an expensive clothing store earns $2600 per month base pay plus a 6.5% commission on sales. One month she earns $5518.50. What were her sales for that month?

Solve. -A brother and sister split the $922,500 from the sale of their parent's house. According to the will, the sister was to receive 25% more than her brother, for having managed the property. How much money did the sister Receive?

Solve. -Logan bought stocks and later sold them for $1,081,600, making a profit of 4%. How much did he pay for the stocks?

Solve. -Ming got a 19% raise in her salary from last year. This year she is earning $135,660. How much did she make last year?

Solve. -Holly bought a sweater on sale for 20% off the original price. If she saved $12, what was the original price?

Solve. -Michael hired Heather to iron his dress shirts. Heather charges $40 an hour plus $0.25 for each shirt ironed. Heather worked 4 hours and sent a bill to Michael for $174. How many shirts did Heather iron?