Suppose you purchase 3 identical T-shirts and a hat. The hat costs $19.75 and you spend $56.50 in all. How much does each T-shirt cost?
We're being asked to figure out the cost of each T-shirt. We know how much was spent and the cost of the other item purchased. Let's do this 2 ways - piece by piece and then all together.
So we know that we spent $56.50 and we bought a hat and 3 T-shirts. The hat was $19.75, so let's take that away from the total spent and that will give us the amount spent on T-shirts:
We bought 3 identical T-shirts, which means that they are all the same price. We can take the 36.75 spent on 3 T-shirts in total, divide by 3, and find the cost of each T-shirt:
Now let's do it all together at once. We know that the amount we spent was for a hat and 3 T-shirts, so we can write that out in an algebraic equation like this:
where S is Spent, H is Hat, and and T is one T-shirt (and so 3T is for 3 T-shirts). We can then substitute in what we know and solve for T:
subtract 19.75 from both sides, then divide by 3: