5 books and 9 magazines cost $150.50 altogether. 9 books and 5 magazines cost $175.70. How much does 1 book and 1 magazine cost?
To find the cost of one book and one magazine, we can set up a system of equations based on the given information.
Let's assign variables to the unknowns:
Let b represent the cost of one book, and let m represent the cost of one magazine.
From the first piece of information, we can form an equation:
5b + 9m = 150.50 Equation (1)
From the second piece of information, we can form another equation:
9b + 5m = 175.70 Equation (2)
Now we have a system of equations with two variables. We can solve this system using either substitution or elimination method.
Let's use the elimination method to solve this system:
Multiply equation (1) by 9 and equation (2) by 5 to make the coefficients of "b" in both equations the same:
45b + 81m = 1354.50 Equation (3)
45b + 25m = 878.50 Equation (4)
Now subtract equation (4) from equation (3):
(45b + 81m) - (45b + 25m) = 1354.50 - 878.50
56m = 476
Divide both sides by 56:
m = 8.50
Now we have the value of m, which represents the cost of one magazine.
Substitute this value back into equation (1) to solve for b:
5b + 9(8.50) = 150.50
5b + 76.50 = 150.50
5b = 74
b = 14.80
Therefore, one book costs $14.80, and one magazine costs $8.50.