Ten bagels and four muffins cost 13$. Five bagels and eight muffins cost 14$. What are the prices of a bagel and a muffin?

Muffins cost $1.25 and bagels cost $0.80.

We know by addition that 15 bagels and 12 muffins would cost $27. We can divide each term by 3 to simplify this and see that 5 bagels and 4 muffins would cost $9. Since we already knew that 5 bagels and 8 muffins cost $14, we can use subtraction to discover that 4 muffins cost $5. By dividing both sides of the equation by 4 we learn that a muffin costs $1.25. Once we know this we can plug this back into any equation to derive the cost of a bagel. For example 10b + (4 x 1.25) = 13, so 10b = 13 - (4 x 1.25), so, b = [13 - (4 x 1.25) ]/10, so b = 0.80.