Question

A bag contains purple marbles and white marbles, 68 in total. The number of purple marbles is 4 less than 5 times the number of white marbles. How many purple marbles are there?

Answer 1

Answer: 56 purple marbles.

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:

`\left \{ {{p+w=68} \atop {p=5w-4}} \right.`

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:

`(5w-4)+w=68`

2. Now you must solve for "w":

`5w-4+w=68\\\\6w-4=68\\\\6w=68+4\\\\6w=72\\\\w=(72)/(6)\\\\w=12`

3. Substitute the value of "w" into second original equation and then evaluate in order to find the value "p":

`p=5(12)-4\\\\p=60-4\\\\p=56`