Question

Liam is a cyclist. He is recovering from an injury, so he is gradually building up his speed and endurance.
Yesterday Liam averaged 12 mph in the first half of a ten-mile training course and 9 mph in the second half of the training course.

What was the percent of decrease in the Liam’s average speed from the first half of the training course to the second half of the training course?
Responses
A
3 percent
B
33 percent
C
75 percent
D
25 percent
Question 2

Last summer Doreen ordered a mega-package of water balloons for her kids. This summer Doreen ordered the same mega-package of water balloons. The package of water balloons that Doreen ordered this summer was $12 more than th one that she ordered last summer. This was a 40% increase in the price.

What was the price of the mega-package of water balloons that Doreen ordered this summer?
Responses
A
48 dollars
B
42 dollars
C
30 dollars
D
18 dollars

Answer 1

To solve both questions, let's analyze them one by one.

### Question 1:
Liam's average speed for the two halves of his training course:
- First half: 12 mph
- Second half: 9 mph

To find the percent decrease in speed from the first half to the second half, we can use the formula for percent decrease:

\[
\text{Percent Decrease} = \frac{\text{Old Value} - \text{New Value}}{\text{Old Value}} \times 100
\]

In this case:
- Old Value (first half speed) = 12 mph
- New Value (second half speed) = 9 mph

Substituting these values into the formula:

\[
\text{Percent Decrease} = \frac{12 - 9}{12} \times 100 = \frac{3}{12} \times 100 = 25\%
\]

So, the answer is **D. 25 percent**.

### Question 2:
Doreen's water balloon package price increase:
Let's denote the price of the package last summer as \( x \). According to the problem:
- This summer's package price = \( x + 12 \)
- This summer's price is a 40% increase compared to last summer, which can be expressed as:

\[
x + 12 = x + 0.4x = 1.4x
\]

Now, we can set up the equation:

\[
x + 12 = 1.4x
\]

Now, solve for \( x \):

\[
12 = 1.4x - x
\]
\[
12 = 0.4x
\]
\[
x = \frac{12}{0.4} = 30
\]

So, the price last summer was $30, and this summer's price is:

\[
30 + 12 = 42
\]

Thus, the price of the mega-package of water balloons that Doreen ordered this summer is **B. 42 dollars**.