Michael sold 200 candy bars in three days. On the first day, he sold of the 12 candy bars. On the second day, he sold 14 of the remaining candy bars. On the third day, he sold the rest of the candy bars. What is the ratio of the number of candy bars Michael sold on the first day to the number he sold on the second day to the number he sold on the third day?

Rationale

The ratio of the number of candy bars Michael sold on the first day to the number he sold on the second day to the number he sold on the third day is 2 to 1 to 1.

Michael sold 12 candy bars on the first day and 14 on the second day. To find the number sold on the third day, we calculate the total sold over the three days, which totals 200 candy bars. Therefore, the amounts sold can be expressed in the ratio of 12:14:(200 - 12 - 14), simplifying to 2:1:1.

A (2 to 1 to 1) CORRECT

This ratio accurately reflects the quantities sold on each day. Michael sold 12 candy bars on the first day, 14 on the second day, and the remainder on the third day, which totals 200 - 12 - 14 = 174. The ratio simplifies to 2:1:1 when the quantities are represented proportionally.

B (2 to 4 to 1) YOUR ANSWER

This option incorrectly suggests that Michael sold 4 times as many candy bars on the second day as on the first day. The actual sales of 12 on the first day and 14 on the second do not support this ratio, as the second day only has a slight increase over the first.

C (3 to 2 to 1) YOUR ANSWER

This ratio implies a distribution of sales that does not align with the actual numbers sold. It suggests that the first day had a much higher count than what was recorded, leading to an incorrect interpretation of the sales figures.

D (4 to 1 to 3) YOUR ANSWER

This choice misrepresents the sales data entirely. It indicates a much higher sales figure for the third day in comparison to the first and second days, contradicting the calculation that shows the third day had a significantly lower number sold.

Conclusion

The correct ratio of candy bars sold by Michael over three days is 2 to 1 to 1, based on the actual sales figures. The first day’s sales of 12 and the second day’s sales of 14 lead to a total that confirms the third day’s sales, validating the calculated ratio. Other options inaccurately represent the sales distribution, reinforcing the importance of precise calculations in determining ratios.

The ratio of the number of candy bars Michael sold on the first day to the number he sold on the second day to the number he sold on the third day is 2 to 1 to 1.

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