COURSE MODULE NAME PERCENTAGES

Solution to Problem 14:
Let S be the total monthly salary and x be the monthly sales, hence
S = 500 + 5% * x
Find sales x so that S = 1500, hence
1500 = 500 + 5% * x = 500 + 0.05 x
Solve for x
x = (1500 - 500) / 0.05 = $20000
15.A chemist has a 20% and a 40% acid solutions. What amount of each solution should be used
in order to make 300 ml of a 28% acid solution?
Solution to Problem 15:
Let x be the solution at 20% and y be the solution at 40%, hence
x + y = 300 ml
We now write an equation that expresses that the total acid in the final 300 ml is
equal to the sum of the amounts of acid in x and y
28% * 300 = 20% * x + 40% * y
Solve the above system of equations to find
x = 180 and y = 120
16.What percent of the total area of the circular disk is colored red?
Solution to Problem 16:
Total area of disk
Ad = pi * r 2
Angle t in radians of central angle of red sector
t = (360-120)* pi / 180 = (4/3) pi
Area of red sector
As = (1/2) t * r 2
Percentage of total area in red
P = [ (1/2) t * r 2 ] / [ pi * r 2 ]
= 4 / 6 = 66.7% (3 significant digits)
THINK: compare 66.7% to 240 / 360, why are they equal?
17.What percent of the total area of the rectangle is colored red?
Percentages
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