A hotel manager found that his gross receipts for the day, including a 5% sales tax, were $1645.35. Find the amount of sales tax collected.

The amount of sales tax collected is $78.35

Step-by-step explanation:

Percentages

The gross receipts for the day were $1645.35, including a 5% sales tax.

If a percentage is already included (added) to a certain quantity, then it's not the original quantity or 100%.

The problem states that the gross receipts already include a 5% sales tax, thus the receipts are 100+5=105% of the net sales.

This means the net sales were $1645.35 / 105 * 100 = $1567

Subtracting $$1645.35 - $1567 = $78.35 we get the amount of sales tax.

The amount of sales tax collected is $78.35

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

~

2/3

step-by-step explanation:

the slope of a line is equal to the rise/run. in this case the line rises 2 units for every +3 units it moves