# Structure And Method: Section 10-3

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Check-in on section 10-3. Writing and solving inequalities.

• 1.

### Chose the correct answer.  Express each quantity in terms of k. The value of quarters in cent of k quarters

• A.

K

• B.

25k

• C.

K + 25

• D.

K/25

B. 25k
Explanation
The value of quarters in cents can be expressed as 25 cents per quarter. Multiplying this by the number of quarters, k, gives us 25k cents.

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• 2.

### Chose the correct answer.  Express each quantity in terms of k. The time needed to travel 100 km at k km/h

• A.

Not enough information given to determine

• B.

K/1000

• C.

100k

• D.

100/k

D. 100/k
Explanation
The time needed to travel 100 km at a speed of k km/h can be expressed as 100/k. This is because the distance (100 km) divided by the speed (k km/h) gives us the time taken to travel that distance.

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• 3.

### Chose the correct answer.  Express each quantity in terms of k. The area of a rectangle measuring 23 m by k m

• A.

2(23) + 2k

• B.

23k

• C.

(23k)(23k)

• D.

23 + k

B. 23k
Explanation
The area of a rectangle is calculated by multiplying its length and width. In this case, the length is given as 23 m and the width is given as k m. Therefore, the area can be expressed as 23k.

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• 4.

### Chose the correct answer.  Express each quantity in terms of k. The cost of a k-minute telephone call, if the first minute costs $0.40 and each additional minute is$0.30

• A.

0.40 + 0.30(k - 1)

• B.

0.40 + 0.30k

• C.

0.30k + k

• D.

0.40k + 0.30(k-1)

A. 0.40 + 0.30(k - 1)
Explanation
The cost of a k-minute telephone call can be calculated by adding the initial cost of $0.40 to the cost of each additional minute. Since each additional minute costs$0.30, we can multiply the number of additional minutes (k - 1) by $0.30 and add it to$0.40 to get the total cost. Therefore, the correct answer is 0.40 + 0.30(k - 1).

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• 5.

### Chose the correct answer.  Express each quantity in terms of k. The perimeter of a rectangle that measures 2.5 ft by k ft

• A.

2.5 + k

• B.

2.5 + 2k

• C.

5 + 2k

• D.

2.5k

C. 5 + 2k
Explanation
The perimeter of a rectangle is calculated by adding the lengths of all its sides. In this case, the rectangle measures 2.5 ft by k ft. The length of one side is 2.5 ft and the length of the other side is k ft. To find the perimeter, we add the lengths of both sides: 2.5 ft + k ft. Therefore, the correct answer is 2.5 + k.

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• 6.

### Chose the correct answer. Mel had $28. After cashing a check he received from his mom, he had more than$75.  What is the amount of the check Mel cashed?

• A.

Mel cashed a check for more than $47. • B. Mel cashed a check for less than$47.

• C.

Mel cashed a check for less than or equal to $47. • D. Mel cashed a check for more than or equal to$47.

A. Mel cashed a check for more than $47. Explanation The given information states that after cashing the check, Mel had more than$75. This means that the amount of the check Mel cashed must be greater than the difference between $75 and the initial$28 he had. The difference is $75 -$28 = $47. Therefore, the check Mel cashed must be for more than$47.

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• 7.

### Choose the correct answer.  Postage is $.25 for the first ounce and$.20 for each additional ounce.  How heavy a package, to the nearest ounce, can Marcella send if she wants to spend no more than $2.25? • A. Marcella can send a package weighing more than 11 ounces. • B. Marcella can send a package weighing less than 11 ounces. • C. Marcella can send a package weighing equal to 11 ounces or less. • D. Marcella can send a package weighing equal to 11 ounces or more. Correct Answer C. Marcella can send a package weighing equal to 11 ounces or less. Explanation Marcella can send a package weighing equal to 11 ounces or less because the first ounce costs$.25 and each additional ounce costs $.20. To spend no more than$2.25, Marcella can pay for the first ounce and then pay for 10 additional ounces, which would cost a total of $2.25. Therefore, the package can weigh up to 11 ounces. Rate this question: • 8. ### Choose the correct answer. The width of a poster is 8 cm less than the length. The perimeter is more than 184 cm. If the measurements are both integers, fund the minimum dimensions of the poster. • A. The minimum dimensions are 102 cm by 86 cm. • B. The minimum dimensions are 51 cm by 59 cm. • C. The minimum dimensions are 43 cm by 35 cm. • D. The minimum dimensions are 51 cm by 43 cm. Correct Answer D. The minimum dimensions are 51 cm by 43 cm. Explanation The width of the poster is 8 cm less than the length, which means that if we let the length be x, then the width would be (x-8). The perimeter is more than 184 cm, so we can set up the equation 2(x + (x-8)) > 184. Simplifying this equation gives us 4x - 16 > 184, which further simplifies to 4x > 200. Dividing both sides by 4 gives us x > 50. Since the dimensions are both integers, the minimum value for x would be 51. Therefore, the minimum dimensions of the poster would be 51 cm by 43 cm. Rate this question: • 9. ### Choose the correct answer. After serving 45 lb of poultry, caterer had more than 10 lb left. How many pounds of poultry did the caterer have originally? • A. More than 55 lb • B. Less than 55 lb • C. 55 lb or more • D. 55 lb or less Correct Answer A. More than 55 lb Explanation Since the caterer had more than 10 lb left after serving 45 lb of poultry, it means that the amount left is greater than 10 lb. Therefore, the original amount of poultry the caterer had must be more than 55 lb, as the caterer had more than 10 lb left after serving 45 lb. Rate this question: • 10. ### Choose the correct answer. Sonya is a waitress. She earns$200 a week plus a 15% tip on the cost of each meal she serves.  What must be the total cost of the meals she serves for her to each at least $425 each week? • A.$1500 or less

• B.

Less than $1500 • C.$1500 or more

• D.

More than $1500 Correct Answer C.$1500 or more
Explanation
Sonya earns $200 a week plus a 15% tip on the cost of each meal she serves. In order for her to earn at least$425 each week, the total amount she earns from tips must be at least $225 ($425 - $200). Since the tip is 15% of the cost of each meal, the total cost of the meals she serves must be at least$1500 ($225 / 0.15). Therefore, the correct answer is$1500 or more.

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• 11.

### Choose the correct answer.  The length of a rectangle is 6 cm shorter than its width.  The perimeter is at least 60 cm.  What are the smallest possible dimensions for the rectangle?

• A.

12 cm by 18 cm

• B.

18 cm by 24 cm

• C.

6 cm by 12 cm

• D.

A. 12 cm by 18 cm
Explanation
The length of the rectangle is 6 cm shorter than its width. If we let the width be x cm, then the length would be x - 6 cm. The perimeter of a rectangle is given by the formula P = 2(length + width). In this case, P = 2(x - 6 + x) = 2(2x - 6) = 4x - 12. We are told that the perimeter is at least 60 cm, so 4x - 12 ≥ 60. Solving this inequality, we get x ≥ 18. Therefore, the smallest possible width is 18 cm. Substituting this value back into the length equation, we get the smallest possible length as 18 - 6 = 12 cm. Hence, the smallest possible dimensions for the rectangle are 12 cm by 18 cm.

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• 12.

### Chose the correct inequality.  The variable represents the number indicated in the parentheses.  Maria, who is older than her 12-year-old brother, is 4 years younger than Sue.  (Sue's age)

A.
Explanation
Maria's age is 4 years younger than Sue's age. Since Maria is older than her 12-year-old brother, we can infer that Sue's age must be greater than 12. Therefore, the correct inequality is Sue's age > 12.

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• 13.

### Chose the correct inequality.  The variable represents the number indicated in the parentheses.  The sum of four consecutive integers is at most 100.  (Smallest integer)

A.
Explanation
The smallest integer can be found by setting up the inequality and solving for the variable. Let's assume the smallest integer is represented by x. Since we are looking for four consecutive integers, the other three integers can be represented by x+1, x+2, and x+3. The sum of these four integers can be expressed as x + (x+1) + (x+2) + (x+3). We know that this sum is at most 100, so we can set up the inequality as follows: x + (x+1) + (x+2) + (x+3) ≤ 100. Simplifying this inequality, we get 4x + 6 ≤ 100. Solving for x, we find that x ≤ 24. Therefore, the smallest integer is 24.

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• 14.

### Chose the correct inequality.  The variable represents the number indicated in the parentheses.  Fred has one third as many $10 bills as$20 bills.  He has at least $300. (Number of$20 bills)

D.
Explanation
Fred has one third as many $10 bills as$20 bills. This can be represented as $10b = \frac{1}{3}(20b), where b represents the number of$20 bills. We are given that Fred has at least $300, so the inequality can be written as$10b + $20b ≥$300. Simplifying this inequality, we get 30b ≥ 300, which further simplifies to b ≥ 10. Therefore, the correct inequality is b ≥ 10.

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• 15.

### Chose the correct answer.  A purse contains 26 coins, some of which are dimes and the rest nickels.  Altogether, the coins are worth more than \$2.10.  At least how many dimes are in the purse?

• A.

At least 16 dimes

• B.

At least 17 dimes

• C.

At least 15 dimes

• D.

Not enough information given to solve

B. At least 17 dimes

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