Question

x+y+z=20 and 20x+8y+z=40 than find the value of x, y, z

Answer 1

X+y+z=100 and 50x+10y+z=500 what is the value of x,y, z?

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3 ANSWERS



Avery Schmidt, Passed Math Class

Answered Feb 21, 2016

x(50) + y(10) + z(1) = 500

Further we know that x+y+z = 100. This gives two independent equations in three unknowns, so we possibly have an under-determined system and multiple solutions (if any are possible). If we had one more equation, life would be better, as I'm sure you already know!

Anyway, 50x + 10y + z = 500 and x+y+z = 100, so:

z = 500 - 50x - 10y

z = 100 - x - y

500 - 50x - 10y = 100 - x - y

400 - 49x - 9y = 0

49x + 9y = 400

9y = 400 - 49x

y = 400/9 - (49/9)x

Both 49 and 9 are the squares of primes, so that's suspicious right away, and indicates 

400/9 - 49x/9 must be a positive whole number. The *only* positive value of x such that this is true is 1, so x *must* equal 1. y = 400/9 - (49/9)x

= 400/9 - 49/9

= 351/9

= 39.

So we have x = 1 and y = 39. We know that x+y+z = 100, so z = 100 - 39 - 1 = 100 - 40 = 60.

There you go.

50*1 + 10*39 + 1*60

= 50 + 390 + 60

= 110 + 390

= 500

Answer 2

Answer:

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