A coffee shop owner blends a gourmet brand of coffee with a cheaper brand. The gourmet coffee usually sells for $9.00 per pound. The cheaper brand sells for $3.00 per pound. How much of each type should be mixed in order to have 40 pounds of coffee that is worth $7.50 per pound?

30 pounds of $9 brand

10 pounds of $3 brand

Step-by-step explanation:

let x = $9 brand

let y = $3 brand

system of equations:

x + y = 40

9x + 3y = 40(7.5)

substitution method:  x = 40 - y

9(40 - y) + 3y = 300

360 - 9y + 3y = 300

360 - 6y = 300

-6y = -60

y = 10

so, x = 40 - 10 or 30

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c