Question

The local frozen yogurt shop determines the total cost of a cup of yogurt using the formula y = 2 + 0.75x, where x represents the number of ounces. If you can spend between $2 and $5, what is the DOMAIN of this situation

Answer 1

Answer: 0 ≤ x ≤ 4

Explanation:

The cost equation can be written as:

y = $2 + $0.75*x

Where x is the number of ounces that you buy.

If you can spend between $2 and $5, then we have the inequality:

$2 ≤ y ≤ $5

replacing y by the above equation:

$2 ≤ $2 + $0.75*x ≤ $5

Now let's solve this for x.

$2 - $2 ≤ ($2 + $0.75*x) - $2 ≤ $5 - $2

$0 ≤ $0.75*x ≤ $3

now we can divide bt $0.75 in the 3 sides:

$0/$0.75 ≤ ($0.75*x)/$0.75 ≤ $3/$0.75

0 ≤ x ≤ 4

Then the domain is:

D: 0 ≤ x ≤ 4

or we can also write this as:

D = x ∈ [0, 4]