Structure And Method: Section 10-3

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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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