### All TACHS Math Resources

## Example Questions

### Example Question #1 : Word Problems

Tim can ride his bike eight miles in one hour. How long will it take him to ride forty miles?

**Possible Answers:**

Cannot be determined

**Correct answer:**

If Tim can ride his bike eight miles in one hour then we can write the following ratio:

Next, we want to know how long it will take him to ride forty miles. We can write the following ratio:

Next, we can set these equal to one another and form a proportion.

Cross multiply and solve for the variable.

Simplify.

Divide each side of the equation by .

Solve.

### Example Question #41 : Math

Barry, Jerry, and Mary order a pizza. Barry pays half the cost; Jerry pays one third of the cost; Mary pays the rest, which is $3. How much did the pizza cost?

**Possible Answers:**

**Correct answer:**

Let be the cost of the pizza. Barry paid half the cost of the pizza, which is ; Jerry paid one third of the cost, which is , and Mary paid $3. The sum of their shares of the cost is equal to the total cost, so the equation to set up is

Solve for by isolating the variable at left. First, at right, collect the like terms by adding the coefficients of . This requires finding the least common denominator of the two fractions, which is 6:

Subtract from both sides, again by collecting like terms:

Now multiply both sides by 6 to reverse multiplication by :

The pizza cost $18.

### Example Question #1 : Solving Multi Step Problems

The first 60 miles of a 100-mile trip took one hour; the whole trip took two hours and fifteen minutes. To the nearest whole, what was the average speed during the remaining 40 miles of the trip?

**Possible Answers:**

32 miles per hour

40 miles per hour

50 miles per hour

36 miles per hour

**Correct answer:**

32 miles per hour

The average speed during a trip of miles over a period of hours is miles per hour. Here, the distance driven is 40 miles; the time it took was two hours and fifteen minutes total minus the hour for the first 40 miles, which is one hour and fifteen minutes. Since fifteen minutes is equal to

hours, we get

and

Therefore, the average speed traveled during the second part of the trip is

miles per hour.

### Example Question #1 : Word Problems

Jeremy has pieces of candy. Maggie has half as many pieces of candy as Jeremy has, and Harold has twice as many pieces of candy as Jeremy and Maggie combined. How many pieces of candy does Harold have?

**Possible Answers:**

**Correct answer:**

Start by finding how many pieces of candy Maggie has. Since she has half as many as Jeremy, she must have pieces. Then, Jeremy and Maggie have pieces of candy together. Since Harold has twice as many as the two of them together, Harold must have pieces of candy.

### Example Question #1 : Solving Multi Step Problems

Taylor is years old. Her father is three times her age. Her mother is two years older than her father. What is the sum of the ages of Taylor, her father, and her mother?

**Possible Answers:**

**Correct answer:**

Start by multiplying Taylor's age by to find her father's age.

Her father must be years old. Since her mother is two years older than her father, her mother must be years old.

Now, add up all their ages to find the sum of their ages.

### Example Question #1 : Word Problems

When Steve started his diet, he weighed pounds. After the first month, he lost of his weight. In his second month, he lost of the remaining weight. How many pounds does Steve weigh now?

**Possible Answers:**

**Correct answer:**

Start by finding how much weight Steve lost after the first month. Since he lost of his starting weight of , he must have lost pounds.

This means that at the end of his first month, he weighed pounds.

Since he lost of his remaining weight in the second month, he must have lost pounds from his pounds.

Thus, Steve must weigh pounds now.

### Example Question #42 : Math

A school library uses shelves that can hold books. If they have shelves that are completely full and one shelf that is only full, how many books does the library have?

**Possible Answers:**

**Correct answer:**

Start by finding out how many books the full shelves can hold by multiplying it by the number of books held per shelf.

Next, find out how many books are held by the shelf that is not completely full.

Now, add the two together to find how many books total are in the library.