A bag contains white marbles and red marbles, 69 in total. The number of white marbles is 1 more than 3 times the number of red marbles. How many white marbles are there?

Answer 1

This question is completed by making a system of equations and combining both in order to find the number of white marbles.

First of all, we can easily make an equation, T = r + w. "T" is the total amount of marbles (both red and white), "r" is the amount of red marbles, and "w" is the amount of white marbles. The other equation we can make is, w = 1 + 3r. In this equation, "w" and "r" are the same variables as the "w" and "r" in the first equation we constructed.

Now, let's remember that both of these equations are not solvable because we do not have enough information to solve them separately. However, we can combine them in order to make an equation where we can actually solve for "w," as the problem asks us to. Rearrange the equation, T = r + w, by subtracting w on both sides, so that the new rearranged equation is r = T - w. Now, we can replace the "r" in w = 1 + 3r with "T-w." Thus, our new combined equation is w = 1 + 3(T-w). Using distributive properties to distribute the 3 to the variables in the parentheses, we know that w = 1 + 3T - 3w. We know that T = 69 since the total amount of marbles is 69, so we can replace the variable "T" with 69 in our equation. Now, we have w = 1 + 3(69) - 3w, meaning w = 208 - 3w. Now that we have "w" on both sides, we can solve the equation by adding "3w" to both sides. Now, we have 4w = 208. Divide both sides by 4, and you should get w = 52.

This means that there are 52 white marbles in the bag.