Question

Vincent and George had 852 notebooks together. Vincent had 210 more notebooks than George. Both of them sold some of their notebooks. George sold 20% less notebooks than what Vincent sold. In the end, George had half as many notebooks left as Vincent. How many notebooks had Vincent left?

Answer 1

x = notebook of Vincent
y = notebook of George

x + y = 852 -> eq. 1
x = 210 + y -> eq. 2
x + y = 852
210 + y + y = 852
y = 321
x = 210 + y
x = 531

a = notebooks sold by Vincent
b = notebooks sold by George

b = a - 0.2a
b = 0.8a
SOLD + REMAINING = TOTAL
For Vincent (V)
v + a = 531
v = 531 - a
For George (G)
g + 0 = 321
g + 0.8a = 321
g = 321 - 0.8a

GEORGE HAD HALF AS MANY LEFT AS VINCENT
v/2 = 6
(531 - 9)/2 = 321 - 0.8a
265.5 - 9(0.5) = 321 - 0.8a
a = 185
b = 0.8a = 148

v = ?
v = 531 - 9
v = 346 notebooks left for vincent

Answer 2

George : x notebooks
Vincent : 852 - x notebooks
852 - x = x + 210
2x = 642
x = 321
-> 852 - 321 = 531
Vincent sold : y notebooks
George sold : (1 - 20%)y = 0.8y notebooks
1/2(531 - y) = 321 - 0.8y
531 - y = 642 - 1.6y
0.6y = 111
y = 185
531 - 185 = 346