23. A sales manager wants to order baseball caps with her company logo for the salespeople attending a weekend training. Unique Uniforms charges $17.75 per cap, plus a design fee of $30. Logo Direct charges $15.50 per cap, plus a delivery fee of $48. For what number of caps ordered, would the cost be the same from both vendors?

the number of caps be 8

Step-by-step explanation:

The computation of the number of caps ordered in order to equal the cost is shown below:

Let us assume the number of cap be x

Now the equations are

17.75x  + $30

15.50x + $48

Now equate these two equations

17.75x + $30 = 15.50x + $48

17.75x - 15.50x = $48 - $30

2.25x = $18

x = 8

Hence, the number of caps be 8

Question 1:

For this case we have that by definition, the GCF of two numbers is the largest number that is a factor of both numbers. For example, the number 10 is the biggest factor that 50 and 30 have in common.

We must find the GCF of the following expression:

We look for the prime factorization of each number:

The GCF of the three numbers is

So:

Option C

Question 2:

For this case we have that by definition of power properties of the same base, that:

That is, for multiplication of powers of the same base, the same base is placed and the exponents are added.

So:

Option A