Question

The total price of a dictionary and an atlas is $16. The total price of 2 dictionaries and 3 atlases is $43. What is the price of each book?

Answer 1

To find the price of each book, we can set up two equations and solve them using substitution or elimination. The price of each dictionary is $5 and the price of each atlas is $11.

Step-by-step explanation:

To find the price of each book, we can set up two equations based on the given information. Let's assume the price of a dictionary is 'x' and the price of an atlas is 'y'. The first equation is x + y = 16, and the second equation is 2x + 3y = 43. We can solve these equations using the method of substitution or elimination to find the values of x and y.

Step-by-step solution:

1. Start with the equation x + y = 16.
2. From the second equation, solve for x: 2x + 3y = 43 -> 2x = 43 - 3y -> x = (43 - 3y) / 2.
3. Substitute the value of x in the first equation: (43 - 3y) / 2 + y = 16.
4. Simplify the equation: 43 - 3y + 2y = 32. Combine like terms and solve for y: -y = -11 -> y = 11.
5. Substitute the value of y in the first equation: x + 11 = 16 -> x = 5.

Therefore, the price of each dictionary is $5 and the price of each atlas is $11.