Linear equations can be useful in modeling situations where there is an unknown value, such as in the problem below.
You buy 6 notebooks and a $2 set of pencils. A friend buys 4 notebooks and an $8 set of pencils for the same amount of money. How much does one notebook cost?
The equation 6x + 2 = 4x + 8 can be used to find x, the cost of one notebook. You can solve the equation to find that a notebook costs $3.
What different ways could you begin to solve the equations given below? Which store would you rather visit to buy supplies? Choose only one to discuss.
In Store A, you can buy 3 notebooks and a $2 set of pencils for the same price as 4 notebooks. How much does a notebook cost at Store A? The equation 3x + 2 = 4x can be used to find x, the cost of 1 notebook.
In Store B, you can buy 2 notebooks and an $11 set of pencils for the same price as 4 notebooks and a $3 set of pencils. How much does a notebook cost at Store B? The equation 2x + 11 = 4x + 3 can be used to find x, the cost of 1 notebook.