6(10+z+3)
= (6)(10 + z +3)
= (6)(10) + (6)(x) + (6)(3)
= 60 + 6x + 18
= 6x + 78
Vocab:
Parallel = same slope
Perpendicular = opposite sign and reciprocal slope
-5/2 opposite and reciprocal = 2/5
Solution: they are perpendicular
Let us start with assuming the amount of coffee worth $20 a pound to be "x" pounds.
Now she wants to mix "x" pounds of $20 coffee with 70 pounds of $90 coffee.
So the mixture would be (x + 70) pounds.
And the value of mixture would be = 20·x + (90)·(70) = (20x + 6300) dollars.
She want to sell this mixture at rate of $30 a pound. Her earning would be = 30·(x + 70) = (30x + 2100) dollars.
We know that the value of mixture would be equal to her earnings.
30x + 2100 = 20x + 6300
30x - 20x = 6300 - 2100
10x = 4200
x = 420
So, 420 pounds of $20 coffee would be used.
