Question

Blue cassettes hold 45 minutes of music. Green cassettes hold 55 minutes of music. If Niko has 16 cassettes containing 830 minutes of music, how many are blue, and how many are green?

Answer 1

Form a pair of linear equations,

x = Blue cassettes
y = Green cassettes

x + y = 16 ==> Equation 1
45x + 55y = 830 ==> Equation 2

x = 16 - y ==> Equation 3
45(16 - y) + 55y = 830
720 - 45y + 55y = 830
10y = 830 - 720
10y = 110
y = 110 / 10
y = 11 Green cassettes

x = 16 - y
x = 16 - 11
x = 5 Blue cassettes

Answer 2

B + g = 16.....b = 16 - g
45b + 55g = 830

45(16 - g) + 55g = 830
720 - 45g + 55g = 830
-45g + 55g = 830 - 720
10g = 110
g = 110/10
g = 11 <=== there are 11 green cassettes

b + g = 16
b + 11 = 16
b = 16 - 11
b = 5 <=== there are 5 blue cassettes