Adeli has a special one day event to celebrate its anniversary. on the day of the event, every eighth customer receives a free drink. every twelfth customer receives a feee sandwich. if 200 customers show up for the event, how many of the customers will received both a free drink and a free sandwich?

We have to find the customers who receive a free drink and a free sandwich separately and then find the common between the two sets of customers

Since every 8th customer receives a free drink, these customers would be 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 192 and 200

Since every 12th customer receives a free sandwich, these customer would be: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180 and 192

So the common customers among the two sets are customers 24, 48, 72, 96, 120, 144, 168 and 192

So the number of common customers are 8 in number

Conclusion: 8 customers will received both a free drink and a free sandwich

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form

14

step-by-step explanation: