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?
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
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
The answer is 42 Samm
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.
To find out how many lights Rufus uses for the play, we need to calculate the total number of lights.
Let's first determine how many lights have filters. We know that half of the lights that Rufus uses are white. Therefore, the total number of lights is twice the number of white lights.
Let's represent the total number of lights as "x." Since half of the lights are white, we have:
White lights = (1/2)x
Now, let's move on to the remaining lights. We are told that 1/3 of the remaining lights have red filters, and 4 lights have blue filters. The 10 lights left have yellow filters.
The number of lights with red filters is (1/3) of the remaining lights after accounting for the white lights. Therefore:
Lights with red filters = (1/3)(x - (1/2)x) = (1/3)(1/2)x = (1/6)x
The total number of lights with blue filters is given as 4.
Finally, we have 10 lights with yellow filters.
To find the total number of lights, we add up the lights with different filters:
Total lights = White lights + Lights with red filters + Lights with blue filters + Lights with yellow filters
Total lights = (1/2)x + (1/6)x + 4 + 10
To simplify the equation, let's find a common denominator for (1/2)x and (1/6)x:
Total lights = (3/6)x + (1/6)x + 14
Total lights = (4/6)x + 14
Total lights = (2/3)x + 14
Since we don't have the value of x, we cannot determine the exact number of lights Rufus uses. However, we can express the number of lights as a general equation: Total lights = (2/3)x + 14.