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Mark R.

Middle and High School Math Teacher for 6 years

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Geometry

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Question:

A diagonal path through a rectangular garden is 32 feet long. The length of the garden is 24 feet. About how many feet wide is the garden?

Mark R.

Answer:

Drawing a picture would be helpful is starting this problem. When drawing the diagonal, we should see two right triangles appear inside the rectangle. We are now going to use Pythagorean Theorem to solve for the missing side. a^2 + b^2 = c^2 is the formula we will use. The length 24 can be either the "a" or "b" terms. We call these the legs. The length 32 will be used as "c." This is the hypotenuse. a^2 + 24^2 = 32^2 a^2 + 576 = 1024 a^2 = 448 At this point, our final step will be to take the square root to both sides. We will round to the nearest tenth. The width of the garden is 21.2 feet.

Pre-Algebra

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Question:

You are flipping a coin and rolling a dice. What is the probability of flipping a heads and rolling either a 3 or 4?

Mark R.

Answer:

This is a compound probability question. First, we need to find the probability of the first outcome happening. There are two possible outcomes when flipping a coin. The probability of flipping heads would be 1 out of 2. Second, we need to find the probability of rolling either a 3 or 4. When rolling a dice, there are 6 possible outcomes. If the question asks to roll either a 3 or 4, that means there are 2 favorable outcomes. Therefore, the probability of rolling either a 3 or 4 is 2 out of 6. The fraction 2/6 can simplify to 1/3. We will then multiply the two probabilities together. So take 1/2 x 1/3. That means the probability is 1/6. As a percent, this would be 16.7%.

Algebra

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Question:

Tim is selling tickets to his high school musical. He sold a total of 38 tickets. If he received $226 and children's tickets are $5 and adult tickets are $7, how many of each did he sell?

Mark R.

Answer:

First, we need to define our variables. Lets call "c" - the number of children tickets sold and "a" - the number of adult tickets sold. Next, we need to come up with two equations. The first equation will be c + a = 38. This represents that total number of tickets sold. The second equation will be 5c + 7a = 226. This is represent an equation that includes the money values. To solve the equation, lets use the elimination method. Multiple the first equation by -5, which be cancel or eliminate our "c" terms. -5c - 5a = -190 5c + 7a = 226 When combining the equations, the "c" terms will cancel and you are left with 2a = 36. Dividing both sides of the equation by 2 will give us an "a" value of 18. To find out the value of "c" plug the 18 back into the first equation and solve for "c." This will make the "c" value 20. The number of adult tickets sold is 18. The amount of children tickets sold is 20.

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