PURPLE MARBLES=P
WHITE MARBLES=W
First, write out an equation showing the number of purple marbles.
P=5W-6
Then, write out the main equation.
W+P=96
W+5W-6=96
Add 6 to both sides.
W+5W=102
6W=102
Divide both sides by 6
W=17
Now that we know there are 17 white marbles, we can go back to the equation about how many purple marbles there are.
P=5W-6
Plug in the value for W, which is 17.
P=5(17)-6
P=85-6
P=79
To make sure your answer is correct, check your work by plugging in the values for P+W=96.
79+17=96
Answer: There are 79 purple marbles.