Logan earned $8 for each dog he walked last summer. This summer, he raised his fee to $9 per dog. Express the change in Logan’s

0.30x represents the expense for the first soda type. 0.35(x+4) signifies the price for the second type of soda. Combine these amounts into an equation structured as:

Cost of Soda A + Cost of Soda B = Total Cost
0.30x + 0.35(x+4)=3.35 --> Expand 0.35(x+4)
0.30x + 0.35x + 1.4 = 3.35 --> Combine the x's and subtract 1.40.65x = 1.95 --> By dividing by 0.65, we find
x = 3

Samir purchases 3 cans of soda priced at 30 cents each and 7 cans (3+4) at 35 cents each. The overall total for Samir's soda is 10 cans.

Answer:

Let’s outline the sets:

Integers: The collection of all whole numbers.

Rational: Numbers that can be expressed as the ratio of two integers.

Natural: The collection of positive integers.

Whole numbers: All the values obtainable by repeatedly adding (or subtracting) 1 to a number.

Thus:

2 qualifies as a:

Whole number, because 1 + 1 = 2 (therefore, it’s also an integer).

We can express 2 as 4/2.

As 2 is the fraction of two integers, it is also considered rational.

Since 2 is positive and an integer, it falls into the category of natural numbers.

Therefore, the number 2 exemplifies all four sets.

If we include a negative example, we can consider -3.

-3 is classified as an integer, is not a whole number, and with 9/-3 = -3, thus it is also a rational number.

Now, addressing the questions:

a) Although a single example can be used across all four sets, I have chosen 2 in this instance.

b) Similarly, I demonstrated that 2, as a positive integer, belongs to all four sets, thus:

Positive integers belong to:

The set of integers.

The set of natural numbers.

The set of rational numbers.

The set of whole numbers.