Arbitrarily choose the types of coins and the number of one type of coin.
Example Solution: q is quarters and n is nickels. System of Equations: 0.25q+0.05n=2.65 q+n=13
Practice makes perfect
This exercise asks us to write a system of equations to represent the given situation. Since linear systems have two variables, we can have two different types of coins. We will arbitrarily choose that our coins are quarters and nickels.
Let q represent the number of quarters we have.
Let n represent the number of nickels we have.
Note that one quarter is $0.25 and one nickel is $0.05. The only restraint on our system is that the total amount of money is $2.65. Let's now write one equation in the system.
0.25 q+ 0.05 n=2.65
The exercise does not dictate how many of each type of coin we have. We can decide this for ourselves by choosing the number of one type of coins. Suppose we have 10 quarters. That means we have 2.50 in quarters. Therefore, we must have 0.15 in nickels, or 3 nickels. This results in 13 total coins. We can represent this with the following equation.
q+ n=13
Finally ,let's combine our equations to get our system of equations.
0.25q+0.05n=2.65 q+n=13
Note that there are infinitely many solutions to this exercise. We just found one possibility.
