Joint method

The joint method is a technique used to solve problems involving two or more variables. It involves creating a system of equations and then solving them simultaneously to find the values of the variables.

For example, consider the problem:

John and Jane have a total of 35 marbles. John has 5 more marbles than Jane. How many marbles does each person have?

To solve this problem using the joint method, we start by defining our variables. Let J be the number of marbles John has, and let J be the number of marbles Jane has. Then we can write two equations:

J + J = 35 (since they have a total of 35 marbles)
J = J + 5 (since John has 5 more marbles than Jane)

We can then solve this system of equations simultaneously. From the second equation, we can isolate J:

J - J = 5
0J = 5
J = 5

Substituting this value of J into the first equation gives us:

5 + J = 35
J = 30

Therefore, John has 30 marbles and Jane has 5 marbles.