Question

At a poster shop, Han paid $15.75 for 3 large posters and 2 small posters of his favorite band. Kiran paid 13.50 for 4 large posters and 1 small poster of his favorite TV shows. Posters of the same size have the s ice. Find the price of a large poster, ×, and the price of a small poster, y.

Answer 1

x = 2.25

y = 4.5

Explanation:

large posters = x

small posters = y

3x + 2y = 15.75......(Equation 1)

4x + y = 13.5.....(Equation 2)

By simplifying Equation 2, we can say that

y = 13.5 - 4x...(Equation 3)

Now, we can substitute the value of y in equation 1

3x + 2(13.5 - 4x) = 15.75

3x + 27 - 8x = 15.75

-5x = 15.75 - 27

-5x = -11.25...(divide both sides by -5)

x = 2.25

Now, we can substitute the value of x in equation 3

y = 13.5 - 4x

y = 13.5 - 4(2.25)

y = 13.5 - 9

y = 4.5

Answer 2

Answer: A large poster is worth $2.25, and a small poster is worth $4.50

Explanation:

x = large poster

y = small poster

1. Set up a system

3x+2y = 15.75

4x+y = 13.5

2. Solve for a variable (I'll do x for example)

y = 13.5-4x

3. Substitute y into the first equation to get x

3x+2(13.5-4x) = 15.75

3x+27-8x = 15.75

5x = 11.25

x = 2.25

4. Substitute x into the second equation to get y

4(2.25)+y = 13.5

9+y = 13.5

y = 4.5