Question

xavier, yaozhou and zara had some beads. xavier and yaozhou had total of 438 beads. xavier and zara had total of 204 beads. youzhou had 3 times as many beads as zara. how many beads did xavier have ?

Answer 1

To solve this problem, we need to set-up algebraic expression. First, use variables to represent the number of beads. 

Let: x = number of Xavier's beads
       y = number of Yaozhou's beads
       z = number of Zara's beads

It is important to note that since we have three unknowns, we should also have three independent equations. Based on the given statements, we have the following three equations:

(1) x + y = 438
(2) x + z = 204
(3) y = 3z

Substitute y in terms of z in equation (1). Then multiply equation (2) with -1. 

x + 3z = 438
-(x + z = 204)
-------------------
      2z = 234
        z = 117

From equation (3),

y = 3(117) = 351

Using equation (1),

x = 438 - 351 = 87

Thus, Xavier had 87 beads.