Linear Algebraic expression to solve the problem

Question

Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 2 more than 4 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 107?

Mark has ___ marbles to sell

Don has ___ marbles to sell

Answer 1

Let's use the variable , m, to represent the number of marbles that Mark has.

Then we can write the following expression to to represent the number of marbles that Don has: 2 + 4m

Since their sum is 107, we can write and solve the following equation to find the number Mark has first:

Mark's marbles + Don's marbles = 107

m + 2 + 4m = 107

Now combine like terms and use inverse operations to solve:

5m + 2 = 107

5m + 2 - 2 = 107 - 2

5m = 105

5m/5 = 105/5

m= 21

Mark has 21 marbles.

Don has 2 + 4 • 21 = 2 + 84 = 86 marbles