Substitute the values of VW and WY into the expression VWWY= VXXZ and into the two given inequalities.
Example Solution:
VX=6 and XZ=9
VX=6 23 and XZ=10
VX=8 and XZ=12
Practice makes perfect
The following expression is true by the Triangle Proportionality Theorem.
VW/WY=VX/XZ
We also know that in our case VX>VW, XZ>WY, VW=4, and WY=6. Let's substitute the values of VW and WY into the above expression and simplify.
We have that VX is equal to two-thirds of XZ. Keep in mind that we are also given two inequalities. Let's rewrite them by substituting VW=4 and WY=6.
lVX>VW and XZ>WY ⇔ lVX>4 and XZ>6
To sum up, the values of VX and XZ must meet three conditions.
VX is equal to two-thirds of XZ.
The value of VX is greater than 4.
The value of XZ is greater than 6.
Now we will find three possible values of VX and XZ. To do it, we will first choose the value of XZ which is greater than 6, then using the first statement we will determine the value of VX. Finally, we will check if the value of VX is greater than 4. Let's try XZ=9.
If XZ=9, then VX=6. We can see that VX>4. Therefore, all three conditions are met. We found our first pair of values! Following the same steps, let's find two more possible pairs of values.
XZ
XZ? >6
2/3XZ
VX
VX? >4
9
✓
2/3( 9)
6
✓
10
✓
2/3( 10)
6 23
✓
12
✓
2/3( 12)
8
✓
Three possible values for VX and XZ are 6 and 9, 6 23 and 10, and 8 and 12, respectively.
