the greatest of 3 numbers is -8 times the smallest , and the remaining number is 10 more than the smallest.Find the the 3 numbers, given that the greastest is 16 times the sum of the others two numbers
Let x = smallest numberOriginally Posted by Panaboy
y = other number
z = greatest number
z= -8(x) -------(i)
y = x +10 -------(ii)
z = 16(x+y) -------(iii)
Substitute the y from (ii) into (iii),
z = 16(x +x+10) = 16(2x +10) = 32x +160 -------(iv)
Substitute the z from (i) into (iv),
-8x = 32x +160
-8x -32x = 160
x = 160/(-40) = -4 -------answer.
So,
y = x+10 = -4+10 = 6 -------answer.
z = -8x = -8(-4) = 32 ---------answer.
Check,
z = 32x +160
32 =? 32(-4) +160
32 =? -128 +160
32 =? 32
Yes, so, OK.