World War 1

Algebra Level 4

During the World War 1, the Germans suffered heavy casualties.
65% of the tanks lost their guns,
75% lost their commander, and
85% lost their track.

If every tank lost at least one of the commander, the gun, or the track, and 15% lost exactly one of these, how many lost all three?

10% 20% 30% 40%

Bisweswar Martha by Bisweswar Martha , 30, India

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1 solution

Let a, b, c, d, e, f, and g as follows:

Thus,

(1) a + d + f + g = 65 a + d + f + g = 65 [65% of the tanks lost their guns]

(2) b + e + f + g = 75 b + e + f + g = 75 [75% lost their commander]

(3) c + d + e + g = 85 c +d + e + g = 85 [85% lost their track]

(4) a + b + c = 15 a + b + c = 15 [15% lost exactly one]

(5) a + b + c + d + e + f + g = 100 a + b + c + d + e + f + g = 100 [total]

Adding the equations (1), (2), and (3) yields:

(6) a + b + c + 2 d + 2 e + 2 f + 3 g = 225. a + b + c + 2d + 2e + 2f + 3g =225.

Subtracting equation (5) in from equation (6) yields

(7) d + e + f + g = 125. d + e + f + g = 125.

Substituting equation (4) in equation (6) yields

(8) 2 d + 2 e + 2 f + 3 g = 210. 2d + 2e + 2f + 3g = 210.

Solving g from equation (7) and (8) gives us

g = 40. g = 40.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

I added in the LaTeX brackets to make the equations look nicer. I like how you don't just give the lines but actually explain what is substituting / subtracting / etc. It's the sort of thing many people abbreviate but it makes the solution easier/faster to read.

Jason Dyer Staff - 4 years, 5 months ago

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