Answer: 56 purple marbles.
Step-by-step explanation:
Let be "p" the number of purple marbles in the bag and "w" the number of white marbles in the bag.
You can set up the following System of equations:
[tex]\left \{ {{p+w=68} \atop {p=5w-4}} \right.[/tex]
You can use the Substitution method to solve the System of equations. The steps are shown below:
1. You need to substitute the second equation into the first equation:
[tex](5w-4)+w=68[/tex]
2. Now you must solve for "w":
[tex]5w-4+w=68\\\\6w-4=68\\\\6w=68+4\\\\6w=72\\\\w=\frac{72}{6}\\\\w=12[/tex]
3. Substitute the value of "w" into second original equation and then evaluate in order to find the value "p":
[tex]p=5(12)-4\\\\p=60-4\\\\p=56[/tex]
