Question

Ten bagels and four muffins cost $22. Five bagels and eight muffins cost $14. What are the rices of a bagel and a muffin?

Answer 1

To find the prices of a bagel and a muffin, set up a system of equations and use the method of elimination to solve. The price of a bagel is $2 and the price of a muffin is $0.50.

Step-by-step explanation:

To solve this problem, we can set up a system of equations to represent the given information. Let's use b to represent the price of a bagel and m to represent the price of a muffin.

We have the following equations:

• 10b + 4m = 22
• 5b + 8m = 14

To solve this system, we can use the method of elimination. Multiply the first equation by 2 and the second equation by -1 to eliminate the b term:

• 20b + 8m = 44
• -5b - 8m = -14

Adding these two equations together, we get:

• 15b = 30

Dividing both sides by 15, we find that b = 2. Substituting this value back into either of the original equations, we can solve for m. Let's use the first equation:

• 10(2) + 4m = 22
• 20 + 4m = 22
• 4m = 2
• m = 0.5

Therefore, the price of a bagel is $2 and the price of a muffin is $0.50.