At the movies jodie buys three regular popcorns and five small drinks for her friends at a cost of $24.50 her friend renee buyd four regular popcorns and three small drinks for her friends at a cost of $23.50 find the individual costs of a regular popcorn and a small drink The final answer should be a regular popcorn is $4 and a small drink is $2.50 but I have no idea how to get that answer. Can someone please explain?

Step-by-step explanation:

24.50 her friend renee buyd four regular popcorns and three small drinks for her friends at a cost of $23.50 find the individual costs of a regular popcorn and a small drink

The final answer should be a regular popcorn is $4 and a small drink is $2.50 but I have no idea how to get that answer. Can someone please explain?

(a) x = 9, (9,4)

(b) x = 1, (1,3)

(c) x = 1 and the graph of f(x) and g(x) intersects at point (1,3)

(d) or x = 9

(e)

Step-by-step explanation:

We are given that ....... (1),and  

........ (2)

Now,  

(a) We have to solve f(x) = 4

⇒

Converting logarithm to exponent form, we get,

⇒ x = 9 (Answer)

Now, the point on the graph of f(x) will be (9,4) (Answer)

(b) We have to solve g(x) = 3

⇒

Converting logarithm to exponent form, we get,

⇒ x = 1 (Answer)

Now, the point on the graph of g(x) will be (1,3) (Answer)

(c) We have to solve f(x) = g(x)

⇒

Now comparing both sides we can write

x + 7 = 3x + 5  

⇒ 2x = 2  

⇒ x = 1 (Answer)

Now, at x = 1,  

So, the graph of f(x) and g(x) intersects at point (1,3) (Answer)

(d) We have to solve (f + g)(x) = 9

⇒

⇒  

⇒

⇒ 3x² + 26x - 477 = 0

⇒ (3x + 53)(3x - 27) = 0

Hence, or x = 9 (Answer)

(e) We have to solve (f - g)(x) = 3

⇒

⇒

⇒

⇒ x + 7 = 24x + 40

⇒ 23x = - 33

⇒ (Answer)