How many more tickets did Larry buy than Jim?
- A. 3
- B. 12
- C. 6
- D. 1
Correct Answer & Rationale
Correct Answer: C
To determine how many more tickets Larry bought than Jim, we need to compare their ticket purchases. If Larry bought 9 tickets and Jim bought 3, the difference is 9 - 3 = 6. Option A (3) is incorrect because it underestimates the difference. Option B (12) is too high, suggesting Larry bought significantly more than he actually did. Option D (1) also miscalculates the difference, indicating a minimal discrepancy. Thus, the accurate difference of 6 aligns with option C, reflecting the true number of tickets Larry purchased over Jim.
To determine how many more tickets Larry bought than Jim, we need to compare their ticket purchases. If Larry bought 9 tickets and Jim bought 3, the difference is 9 - 3 = 6. Option A (3) is incorrect because it underestimates the difference. Option B (12) is too high, suggesting Larry bought significantly more than he actually did. Option D (1) also miscalculates the difference, indicating a minimal discrepancy. Thus, the accurate difference of 6 aligns with option C, reflecting the true number of tickets Larry purchased over Jim.
Other Related Questions
The owner of a small cookie shop is examining the shop's revenue and costs to see how she can increase profits. Currently, the shop has expenses of $41.26 and $0.19 per cookie.
The shop's revenue and profit depend on the sales price of the cookies. The daily revenue is given in the graph below, where x is the sales price of the cookies and y is the expected revenue at that price.
The shop owner needs to determine the total daily cost of making x cookies. Which of the following linear equations represents the cost, C, in dollars?
- A. C=4.6x+995
- B. C=0.046x+2
- C. C=0.19x+41.26
- D. C=1.2x+212.26
Correct Answer & Rationale
Correct Answer: C
The equation representing total daily cost must account for both fixed and variable costs. The fixed cost of $41.26 reflects the shop's expenses, while the variable cost is $0.19 per cookie, leading to the term 0.19x for x cookies. Therefore, C = 0.19x + 41.26 accurately captures both components. Option A incorrectly suggests a much higher fixed cost and variable rate, implying unrealistic expenses. Option B has a fixed cost that is too low and a variable cost that is also incorrect. Option D presents exaggerated figures for both fixed and variable costs, misrepresenting the shop's actual expenses.
The equation representing total daily cost must account for both fixed and variable costs. The fixed cost of $41.26 reflects the shop's expenses, while the variable cost is $0.19 per cookie, leading to the term 0.19x for x cookies. Therefore, C = 0.19x + 41.26 accurately captures both components. Option A incorrectly suggests a much higher fixed cost and variable rate, implying unrealistic expenses. Option B has a fixed cost that is too low and a variable cost that is also incorrect. Option D presents exaggerated figures for both fixed and variable costs, misrepresenting the shop's actual expenses.
A landscape worker is building a rock wall around a triangular flower garden. He has completed the rock wall on two sides of the garden.
The perimeter of the garden is 239 feet. What is the length, in feet, of the rock wall that the worker still needs to complete?
- A. 101
- B. 185
- C. 54
- D. 138
Correct Answer & Rationale
Correct Answer: D
To determine the length of the rock wall still needed, first, the total perimeter of the triangular garden is 239 feet. The worker has already completed two sides, leaving one side to be built. To find the length of the remaining side, we subtract the lengths of the two completed sides from the total perimeter. The answer of 138 feet indicates that the lengths of the two sides combined equal 101 feet (239 - 138 = 101). Option A (101) represents the combined length of the two completed sides, not the remaining side. Option B (185) exceeds the total perimeter, which is impossible. Option C (54) does not fit the calculations based on the perimeter. Thus, only option D accurately reflects the length of the remaining side to complete the wall.
To determine the length of the rock wall still needed, first, the total perimeter of the triangular garden is 239 feet. The worker has already completed two sides, leaving one side to be built. To find the length of the remaining side, we subtract the lengths of the two completed sides from the total perimeter. The answer of 138 feet indicates that the lengths of the two sides combined equal 101 feet (239 - 138 = 101). Option A (101) represents the combined length of the two completed sides, not the remaining side. Option B (185) exceeds the total perimeter, which is impossible. Option C (54) does not fit the calculations based on the perimeter. Thus, only option D accurately reflects the length of the remaining side to complete the wall.
Which graph shows a line described by 4x - 3y = 12?
- A. M-97A.png
- B. M-97B.png
- C. M-97C.png
- D. M-97D.png
Correct Answer & Rationale
Correct Answer: D
To determine which graph represents the line described by the equation 4x - 3y = 12, we can rearrange it into slope-intercept form (y = mx + b). This yields y = (4/3)x - 4. The slope (m) is 4/3, indicating the line rises 4 units for every 3 units it runs to the right, and the y-intercept (b) is -4, meaning the line crosses the y-axis at (0, -4). Option D correctly displays a line with a positive slope and a y-intercept at -4. Options A, B, and C either have the wrong slope or intercept, indicating they do not accurately represent the given equation.
To determine which graph represents the line described by the equation 4x - 3y = 12, we can rearrange it into slope-intercept form (y = mx + b). This yields y = (4/3)x - 4. The slope (m) is 4/3, indicating the line rises 4 units for every 3 units it runs to the right, and the y-intercept (b) is -4, meaning the line crosses the y-axis at (0, -4). Option D correctly displays a line with a positive slope and a y-intercept at -4. Options A, B, and C either have the wrong slope or intercept, indicating they do not accurately represent the given equation.
Laura walks every evening on the edges of a sports field near her house. The field is in the shape of a rectangle 300 feet (ft) long and 200 ft wide, so 1 lap on the edges of the field is 1,000 ft. She enters through a gate at point G, located exactly halfway along the length of the field.
Laura counts the number of strides she takes during her daily walks. She takes about 80 strides to walk the width of the field from Z to W. Assuming that her stride length does not change, about how many strides does Laura take to walk all the way around the edge of the field?
- A. 267
- B. 320
- C. 450
- D. 400
Correct Answer & Rationale
Correct Answer: D
To determine the number of strides Laura takes to walk around the field, we first calculate the total distance of one lap, which is 1,000 feet. Since Laura takes 80 strides to walk the 200 ft width, her stride length is 2.5 ft (200 ft ÷ 80 strides). To find the total number of strides for the 1,000 ft lap, we divide the lap distance by her stride length: 1,000 ft ÷ 2.5 ft/stride = 400 strides. Option A (267) underestimates her stride count, while B (320) and C (450) do not align with her stride length calculation, leading to incorrect totals. Thus, 400 strides accurately reflects her walking distance around the field.
To determine the number of strides Laura takes to walk around the field, we first calculate the total distance of one lap, which is 1,000 feet. Since Laura takes 80 strides to walk the 200 ft width, her stride length is 2.5 ft (200 ft ÷ 80 strides). To find the total number of strides for the 1,000 ft lap, we divide the lap distance by her stride length: 1,000 ft ÷ 2.5 ft/stride = 400 strides. Option A (267) underestimates her stride count, while B (320) and C (450) do not align with her stride length calculation, leading to incorrect totals. Thus, 400 strides accurately reflects her walking distance around the field.