Question 293451
Let x be the no of share per $3.25
Let y be no of share per $4.50

x + y = 500               --------- (1)
3.25x + 4.50y = 1775      --------- (2)

Multiply equation (1) by 4.50 we get

4.50x + 4.50y = 2250      --------- (3)
3.25x + 4.50y = 1775

Subtract (3) - (2)

1.25x = 475
    x = 475/1.25
    x = 380

x = 380 plugging in (1) we get

x + y = 500
380 + y = 500
      y = 500 - 380
      y = 120

Number of shares he purchased 380 and 120.