The ratio of football cards to baseball cards is 3:2 and the ratio of baseball cards to basketball cards is 3:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 9:6 and the ratio of baseball cards to basketball cards as 6:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 9:6, 6:2 which reduces to 9:2.

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

The factors of a number are all positive integers that divide evenly into the number. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.

To add these radicals together their radicands must be the same:

3\( \sqrt{50} \) + 2\( \sqrt{2} \)
3\( \sqrt{25 \times 2} \) + 2\( \sqrt{2} \)
3\( \sqrt{5^2 \times 2} \) + 2\( \sqrt{2} \)
(3)(5)\( \sqrt{2} \) + 2\( \sqrt{2} \)
15\( \sqrt{2} \) + 2\( \sqrt{2} \)

Now that the radicands are identical, you can add them together:

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 75mph \times 3h \)
225 miles