Set up an equation where you add the same unknown number (x) to both the numerator and the denominator of the original fraction, and set the equation equal to .

Cross-multiply the fractions to simplify.

Now, solve for x.

Because all the numbers are expressed in terms of the smallest number, let that number be represented by x. Therefore, the largest number can be expressed as 4x-6, and the middle number can be expressed as 2x+3. Plug those numbers into the addition equation and solve for x. Then plug the value for x into the expression representing the largest number.

2(4x-6) + (3+3(2x+3)) + 4(x) = 90 --> 18x = 90 --> x = 5

4(6)-6 = 14

The definition of a rational number is an integer or a fraction. We can take the fractions 3/2, 4/3, 5/4, 6/5, 7/6, 8/7,...and continue in this way to realize there are infinitely many rational numbers.

Divide the total money spent by the cost of each painting.

Therefore, to make a profit, she needs to sell more than this amount. Since she can't sell a portion of a painting, the answer has to be the next nearest whole number ().

First, find the total amount of gas necessary for the trip. 6363/63 = 101 gallons (easy to see as 63 * 100 = 6300 + 1 * 63 = 6363). Then multiply the number of gallons by the price per gallon of gasoline, 5.05 * 101 = \$510.05 and is your answer (again, easy to see when 5.05 * 100 + 1 * 5.05).

Because all the numbers are expressed in terms of the smallest number, let that number be represented by x. Therefore, the largest number can be expressed as 4x-6, and the middle number can be expressed as 2x+3. Plug those numbers into the addition equation and solve for x. Then plug the value for x into the expression representing the largest number.

2(4x-6) + (3+3(2x+3)) + 4(x) = 90 --> 18x = 90 --> x = 5

4(6)-6 = 14

Because all the numbers are expressed in terms of the smallest number, let that number be represented by x. Therefore, the largest number can be expressed as 4x-6, and the middle number can be expressed as 2x+3. Plug those numbers into the addition equation and solve for x. Then plug the value for x into the expression representing the largest number.

2(4x-6) + (3+3(2x+3)) + 4(x) = 90 --> 18x = 90 --> x = 5

4(6)-6 = 14

Divide the total money spent by the cost of each painting.

Therefore, to make a profit, she needs to sell more than this amount. Since she can't sell a portion of a painting, the answer has to be the next nearest whole number ().

Recall that in general

Now, let's gather our three rates:

Rate 1:

Rate 2:

Rate 3:

Now, we know that the time is a total of hours. Based on our data, we can write:

This is miles per hour, which rounds to .

Multiply the numerators 2 x 6 x 4 = 48. Then multiply the denominators 3 x 8 x 12 = 288. The answer is 48/288. To simplify, divide both numerator and denominator by 48 to get 1/6.