Martha is playing with Lego. She has 300 of each type - 2spot, 4spot, 8spot. Some bricks used to make zombie. Uses 2spots, 4spots, 8spots in ratio 3:1:2 when finished has twice as many 4spots left as 2spot. How many 8spots are left?

1 Answer
Mar 10, 2018

Remaining 8 spot count is 225

Explanation:

Let the identifier for type 2 spot be S_2 larr 300 at start
Let the identifier for type 4 spot be S_4 larr300 at start
Let the identifier for type 8 spot be S_8larr 300 at start

Zombie -> S_2:S_4:S_8 -> 3:2:1

Left over: S_2:S_4:S_8 -> 1:2:?
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Notice that we have:
color(Brown)("As a guess")

zombiecolor(white)("dd")->3:2:1
remainingul(->1:2:?)
color(white)("ddddddd")->4:4:?

As the vertical sum of all the different type ratios had the same value I suspect the last ratio value for the remaining will have to be 3. Giving a remaining of 1:2:3. As it turns out that is correct.

Building the system in Excel has shown that there is 75 zombies to be made to give a remaining 1:2 ratio of the 2 spot to 4 spot. How this works will be demonstrated later. The remaining 8 spot is 226.

color(white)("d.")1:2
obrace(75: 150): 225 remaining. Note that 3xx75=225
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color(blue)("The mathematical solution")

color(brown)("Method")

Accumulate the 'zombie' ratio count and subtract it from the total.

The remaining has to have the ratio ("2 spot")/("4 spot")-> 1/2

color(brown)("Building the relationship")

color(brown)("Let the count of 'zombies' be "x)

The accumulated zombie (S_2)/(S_4) -> 3/2xx1=3/2xx x/x =(3x)/(2x)

The remaining is (300-3x)/(300-2x)

As a ratio this has to match: (300-3x)/(300-2x) =1/2
Cross multiply

(2(300-3x)=1(300-2x)

600-6x=300-2x

4x=300

x=300/4=75 color(red)(larr "The total zombie count")
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color(blue)("Remaining count of 8 spot")

75 zombies at: S_2:S_4:S_8 -> 3:2:1

Have used a count of 75 as 8 spot bricks for the zombies

Remaining 8 spot -> 300-75 = 225

Tony BTony B