Another kind of modeling that you may see uses symbols to stand for quantities without writing equations. Here is a problem to consider.

Juan and his brother Robert both collect old coins. Together, the two brothers have 15 old coins. Juan has 7 more than Robert. How many coins does each brother have?

To solve this problem, you might choose to use symbols for Juan and Robert and a circle for the coins.

Another way to solve equations is to add or subtract the equations together. When you add these two equations, you get an equation like this: 2J + R = R + 22

Since there is R on both sides of the equation, we can subtract R on both sides and get this equation: 2J = 22.

If you then divide by 2, you get J = 11. So how many did Roberto have? Juan had 7 more so Roberto must have had 4. Can you check that four is correct with the other information in the problem? Yes, since Juan and Roberto had 15, 11 plus 4 is 15.