1. **State the problem:** We are given a histogram showing the frequency density of Roman coins by their mass intervals. We know that 144 coins weigh between 8 g and 17 g, and we need to find the total number of coins in the museum's collection. 2. **Recall the formula:** The number of coins in an interval is given by: $$\text{Number of coins} = \text{Frequency density} \times \text{Width of the interval}$$ 3. **Calculate the number of coins in the 8 g to 17 g interval:** - Frequency density = 2 - Width = 17 - 8 = 9 g So, $$\text{Number} = 2 \times 9 = 18$$ But the problem states there are actually 144 coins in this interval, so the histogram's frequency density scale must be scaled by a factor to match this. 4. **Find the scale factor:** $$\text{Scale factor} = \frac{144}{18} = 8$$ 5. **Calculate the number of coins in each interval using the scale factor:** - Interval 5 to 8 g: frequency density = 6, width = 3 $$\text{Number} = 6 \times 3 = 18$$ Scaled: $$18 \times 8 = 144$$ - Interval 8 to 17 g: already given as 144 - Interval 17 to 22 g: frequency density = 4, width = 5 $$\text{Number} = 4 \times 5 = 20$$ Scaled: $$20 \times 8 = 160$$ - Intervals 0 to 5 g and 22 to 25 g have frequency density 0, so number of coins is 0. 6. **Find total number of coins:** $$144 + 144 + 160 = 448$$ **Final answer:** There are 448 Roman coins in the museum's collection in total.