Question

Rufus is in charge of lighting a play. Half the lights he uses are white. Of the remaining lights, 1/3 have red filters, and 4 have blue filters. The 10 lights left have yellow filters. How many lights does Rufus use for the play?

Answer 1

42. You split the total in half, one half is white the other half has 1/3 red filters meaning the 4 blue filters and 10 yellow filters represent 2/3. We now know that 1/3 of half of the lights is 7. 21 is one half of the lights 2 halves is 42.

Answer 2

Using proper algebra:

number of lights --- x
white = x/2
red = (1/3)(x/2) = x/6
blue = 4
yellow = 10

x/2 + x/6 + 4 + 10 = x
times 6

3x + x + 6(14) = 6x
84 = 2x
x = 42

42 lights in total

check:
whites = 21
leaves 21
red = (1/3)of 21 = 7

sum = 21 whites + 7 red + 4 blue + 10 yello
= 42

Answer 3

The answer is 67

Answer 4

The answer is 42 Samm

Answer 5

You just do:
1/2 x 1/3 = 1/6
1/2 = 3/6
3/6 + 1/6 = 4/6
6/6 - 4/6 = 2/6
2/6 = 14/x
x = 42