Question

At a poster shop, Han paid $15 for 2 large posters and 1 small posters of his favorite band. Kiran paid $18 for 1 large poster and 4 small posters of his favorite TV shows. Posters of the same size have the same price.

Find the price of a large poster, x, and the price of a small poster, y.

Answer 1

The price of a large poster is $6.1875, and the price of a small poster is $2.625, found by setting up and solving a system of linear equations.

Step-by-step explanation:

We have two equations based on the information provided:

1. Han paid $15 for 2 large posters and 1 small poster: 2x + y = 15
2. Kiran paid $18 for 1 large poster and 4 small posters: x + 4y = 18

To find the price of a large poster (x) and the price of a small poster (y), we can use these two equations to set up a system of linear equations and solve for x and y.

Step-by-Step Solution:

1. Multiply the second equation by 2 to eliminate y when added to the first equation:
   2(x + 4y) = 2(18)
   2x + 8y = 36
2. Add the first equation to the new form of the second equation:
   2x + y + 2x + 8y = 15 + 36
   4x + 9y = 51
3. Subtract the original first equation from this new equation:
   (4x + 9y) - (2x + y) = 51 - 15
   2x + 8y - 2x - y = 36 - 15
   8y = 36 - 15
   8y = 21
4. Now, solve for y:
   y = 21/8
   y = 2.625
5. Use the value of y to solve for x in one of the original equations:
   2x + 2.625 = 15
   2x = 15 - 2.625
   2x = 12.375
6. Solve for x:
   x = 12.375/2
   x = 6.1875

Therefore, the price of a large poster (x) is $6.1875, and the price of a small poster (y) is $2.625.