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.

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.

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.

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.

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.

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.

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.

In order to estimate the number of students in class, you will need to round the average number of students in a class up to  and round the number of classes being held down to  also.

Thus,  is easily doable in your head.

There are an estimated  students in class at any given time.