Question

There were 80 skiers and 60 snowboarders on a mountain one day. The next day, the number of skiers decreased by 25%, and the number of snowboarders increased by 5%.

emphasis,Part A,end emphasis,
Which proportion can be used to determine the number of skiers, x, on the mountain the second day?
Question 1 Answer options with 5 options
A.
StartFraction 80 over x EndFraction equals StartFraction 100 over 5 EndFraction
B.
StartFraction 80 over x EndFraction equals StartFraction 100 over 25 EndFraction
C.
StartFraction 80 over x EndFraction equals StartFraction 100 over 60 EndFraction
D.
StartFraction 80 over x EndFraction equals StartFraction 100 over 75 EndFraction
E.
StartFraction 80 over x EndFraction equals StartFraction 100 over 125 EndFraction

emphasis,Part B,end emphasis,
By what percent did the overall number of skiers and snowboarders on the mountain decrease from the first day to the second day? Enter the answer in the box. Round the answer to the nearest percent.

The overall number of skiers and snowboarders decreased bypercent.

Answer 1

To solve Part A, we need to determine how many skiers are present on the mountain after a 25% decrease.

Initially, there are 80 skiers. A 25% decrease means that skiers on the second day will be:

\[
x = 80 - (0.25 \times 80) = 80 - 20 = 60
\]

To find the proportion that can be used to determine this, we can establish the relationship between the original number of skiers and the new number of skiers after the decrease:

\[
\frac{80}{x} = \frac{100}{75}
\]

Here, 75 represents the percent of skiers left after the 25% decrease (100% - 25% = 75%).

So, the correct answer for Part A is:

**D. \(\frac{80}{x} = \frac{100}{75}\)**

---

Now, for Part B, we need to calculate the overall change in the total number of skiers and snowboarders from the first day to the second day.

On the first day:
- Skiers = 80
- Snowboarders = 60
- Total on the first day = 80 + 60 = 140

On the second day:
- Skiers (after 25% decrease) = 60
- Snowboarders (after 5% increase) = 60 + (0.05 \times 60) = 60 + 3 = 63
- Total on the second day = 60 + 63 = 123

Now, we can determine the overall change in total number of skiers and snowboarders:

\[
\text{Decrease} = 140 - 123 = 17
\]

To find the percent decrease:

\[
\text{Percent Decrease} = \left(\frac{\text{Decrease}}{\text{Original total}} \times 100\right) = \left(\frac{17}{140} \times 100\right) \approx 12.14\%
\]

Rounding to the nearest percent gives:

**The overall number of skiers and snowboarders decreased by 12%.**