We are given a few math problems. Problem 2: 65% of children at a party liked chocolate cake. 25 children didn't like chocolate cake. How many children were at the party? Problem 3: A car travels 1 mile per minute. How far does it travel in 1 hour? Problem 4: A rectangular prism is 5 feet long, 4 feet wide, and 8 feet high. Find the volume. Problem 5: Multiply $(3.6 \times 10^{-2})$ by $(1.2 \times 10^6)$ and write the product in scientific notation.

1. Problem Description

We are given a few math problems.

Problem 2: 65% of children at a party liked chocolate cake. 25 children didn't like chocolate cake. How many children were at the party?

Problem 3: A car travels 1 mile per minute. How far does it travel in 1 hour?

Problem 4: A rectangular prism is 5 feet long, 4 feet wide, and 8 feet high. Find the volume.

Problem 5: Multiply $(3.6 \times 10^{-2})$ by $(1.2 \times 10^6)$ and write the product in scientific notation.

2. Solution Steps

Problem 2:

Let $x$ be the total number of children at the party.

Since 65% liked the chocolate cake, 35% did not like it.

We are given that 25 children did not like the chocolate cake, so 35% of $x$ is

2

5. $0.35x = 25$

$x = \frac{25}{0.35} = \frac{2500}{35} = \frac{500}{7} \approx 71.43$

Since the number of children must be an integer, we can round to the nearest integer. However, if we suppose that this is supposed to be an exact result, we must reconsider the problem statement.

If we assume that 35% represents a fraction, then we can say that $35/100$ of the children did not like the cake, that is $7/20$. So $7/20$ of $x$ is

2

5. $\frac{7}{20}x = 25$

$x = \frac{25 \times 20}{7} = \frac{500}{7} \approx 71.43$

If the problem stated that exactly 65% of the children liked chocolate cake, then there must be a mistake, since the answer must be an integer. If we round this up to the nearest integer, that will be

7

2.

However, assuming that we can assume that we can replace 65% with some nearby value that yields an integer answer, then consider a case where 25% do not like chocolate cake. In that case $0.25 x = 25$, so $x=100$. Then 75 children like the chocolate cake. In this case, 75% liked the chocolate cake, close to the 65% from the statement.

Problem 3:

The car travels 1 mile per minute.

There are 60 minutes in 1 hour.

Therefore, the car travels $1 \times 60 = 60$ miles in 1 hour.

Problem 4:

The volume of a rectangular prism is given by:

$V = l \times w \times h$

where $l$ is the length, $w$ is the width, and $h$ is the height.

In this case, $l = 5$ feet, $w = 4$ feet, and $h = 8$ feet.

$V = 5 \times 4 \times 8 = 20 \times 8 = 160$ cubic feet.

Problem 5:

$(3.6 \times 10^{-2}) (1.2 \times 10^6) = (3.6 \times 1.2) \times (10^{-2} \times 10^6)$

$3.6 \times 1.2 = 4.32$

$10^{-2} \times 10^6 = 10^{-2+6} = 10^4$

So, $(3.6 \times 10^{-2}) (1.2 \times 10^6) = 4.32 \times 10^4$

3. Final Answer

Problem 2: $\frac{500}{7}$ children (approximately 71 if the number of children must be an integer).

Problem 3: 60 miles

Problem 4: 160 cubic feet

Problem 5: $4.32 \times 10^4$