If the combined amount of donations collected by Kevin, Fran, and Brooke exceeded the amount Lamar collected by $250, what was the total amount of donations collected by all five club members?
- A. $500
- B. $1,200
- C. $2,500
- D. $3,200
Correct Answer & Rationale
Correct Answer: C
To determine the total amount of donations collected by all five club members, we start with the information that the combined donations of Kevin, Fran, and Brooke exceeded Lamar's by $250. If we denote Lamar's donations as \( L \), then the amount collected by Kevin, Fran, and Brooke is \( L + 250 \). Thus, the total donations from all five members can be expressed as \( L + (L + 250) = 2L + 250 \). To find a plausible total, we consider the options. - A: $500 is too low, as it doesn't allow for both \( L \) and the excess amount. - B: $1,200 also falls short since it would imply \( L \) is negative. - D: $3,200 would require \( L \) to be too high, exceeding reasonable donation limits. C: $2,500 fits perfectly, allowing \( L \) to be $1,125, which is a feasible figure. Therefore, the total amount is logically $2,500.
To determine the total amount of donations collected by all five club members, we start with the information that the combined donations of Kevin, Fran, and Brooke exceeded Lamar's by $250. If we denote Lamar's donations as \( L \), then the amount collected by Kevin, Fran, and Brooke is \( L + 250 \). Thus, the total donations from all five members can be expressed as \( L + (L + 250) = 2L + 250 \). To find a plausible total, we consider the options. - A: $500 is too low, as it doesn't allow for both \( L \) and the excess amount. - B: $1,200 also falls short since it would imply \( L \) is negative. - D: $3,200 would require \( L \) to be too high, exceeding reasonable donation limits. C: $2,500 fits perfectly, allowing \( L \) to be $1,125, which is a feasible figure. Therefore, the total amount is logically $2,500.
Other Related Questions
Which of the following could be the function graphed above?
- A. f(x)=x+1
- B. f(x)=x-1
- C. f(x)=|x|+1
- D. f(x)=x-1
Correct Answer & Rationale
Correct Answer: C
Option C, \( f(x) = |x| + 1 \), accurately represents a V-shaped graph that opens upwards, with its vertex at (0, 1). This aligns with the characteristics of the graph shown. Option A, \( f(x) = x + 1 \), is a linear function with a slope of 1, resulting in a straight line, which does not match the V-shape. Option B, \( f(x) = x - 1 \), is another linear function with a slope of 1, also producing a straight line that does not fit the graph. Option D, \( f(x) = x - 1 \), is identical to Option B and shares the same linear characteristics, further confirming it cannot represent the V-shaped graph.
Option C, \( f(x) = |x| + 1 \), accurately represents a V-shaped graph that opens upwards, with its vertex at (0, 1). This aligns with the characteristics of the graph shown. Option A, \( f(x) = x + 1 \), is a linear function with a slope of 1, resulting in a straight line, which does not match the V-shape. Option B, \( f(x) = x - 1 \), is another linear function with a slope of 1, also producing a straight line that does not fit the graph. Option D, \( f(x) = x - 1 \), is identical to Option B and shares the same linear characteristics, further confirming it cannot represent the V-shaped graph.
The average of 5 numbers is 11. Which of the following must be true?
- A. The range of the 5 numbers is 55.
- B. The sum of the 5 numbers is 55.
- C. The median of 5 numbers is 11.
- D. The mode of 5 numbers is 11.
Correct Answer & Rationale
Correct Answer: B
To find the average of 5 numbers, you sum them and divide by 5. If the average is 11, the total sum must be 5 times 11, which equals 55. Thus, option B is true. Option A is incorrect; the range is the difference between the highest and lowest numbers, which can vary regardless of the average. Option C is also not necessarily true; the median, or middle value, can differ from the average depending on the distribution of the numbers. Option D is incorrect; the mode, or most frequently occurring number, does not have to be the same as the average.
To find the average of 5 numbers, you sum them and divide by 5. If the average is 11, the total sum must be 5 times 11, which equals 55. Thus, option B is true. Option A is incorrect; the range is the difference between the highest and lowest numbers, which can vary regardless of the average. Option C is also not necessarily true; the median, or middle value, can differ from the average depending on the distribution of the numbers. Option D is incorrect; the mode, or most frequently occurring number, does not have to be the same as the average.
How many cups of peanut butter must be used in order to make exactly enough peanut butter balls for the children at the party?
- A. 10
- B. 12
- C. 18
- D. 24
Correct Answer & Rationale
Correct Answer: C
To determine the number of cups of peanut butter needed for the peanut butter balls, one must consider the recipe's requirements and the number of children attending the party. Option C (18 cups) aligns with the recipe's proportion to yield the exact quantity necessary for all children. Option A (10 cups) is insufficient, likely resulting in fewer peanut butter balls than required. Option B (12 cups) may also fall short, leading to a shortage. Option D (24 cups) exceeds the needed amount, creating waste. Thus, C is the optimal choice, ensuring each child receives a peanut butter ball without excess or deficit.
To determine the number of cups of peanut butter needed for the peanut butter balls, one must consider the recipe's requirements and the number of children attending the party. Option C (18 cups) aligns with the recipe's proportion to yield the exact quantity necessary for all children. Option A (10 cups) is insufficient, likely resulting in fewer peanut butter balls than required. Option B (12 cups) may also fall short, leading to a shortage. Option D (24 cups) exceeds the needed amount, creating waste. Thus, C is the optimal choice, ensuring each child receives a peanut butter ball without excess or deficit.
During a sale, the regular price of a pair of running shoes is reduced by 20 percent. $64.00, what is the regular price of the running shoes?
- A. $48.00
- B. $51.20
- C. $76.80
- D. $80.00
Correct Answer & Rationale
Correct Answer: D
To find the regular price of the running shoes, we need to determine what amount, when reduced by 20%, equals $64.00. This can be calculated using the formula: Sale Price = Regular Price × (1 - Discount Rate). Here, the discount rate is 20%, or 0.20. Therefore, the equation becomes $64.00 = Regular Price × 0.80. Solving for Regular Price gives us $64.00 / 0.80 = $80.00. Option A ($48.00) is incorrect because it suggests a much larger discount than 20%. Option B ($51.20) miscalculates the reduction, indicating a 36% discount. Option C ($76.80) inaccurately reflects a smaller discount, resulting in an incorrect sale price. Thus, only option D correctly represents the regular price before the 20% reduction.
To find the regular price of the running shoes, we need to determine what amount, when reduced by 20%, equals $64.00. This can be calculated using the formula: Sale Price = Regular Price × (1 - Discount Rate). Here, the discount rate is 20%, or 0.20. Therefore, the equation becomes $64.00 = Regular Price × 0.80. Solving for Regular Price gives us $64.00 / 0.80 = $80.00. Option A ($48.00) is incorrect because it suggests a much larger discount than 20%. Option B ($51.20) miscalculates the reduction, indicating a 36% discount. Option C ($76.80) inaccurately reflects a smaller discount, resulting in an incorrect sale price. Thus, only option D correctly represents the regular price before the 20% reduction.