x in terms of y?

Question

1. When Max recieved 10x tapes, he then had 5y + 1 times as many tapes as ge had orginally. In terms of x and y, how many tapes did Stanley have originally?
1. 10x(5y + 1) 2. 5y + 1 over 10x 3. 2x over y 4. 10 over 5y + 1 or 5. None of the above

I got 3 but I'm not sure if it's right.

2. If x>0 and y>0 and x^9=4 and x^7 = 9 over y^2, which of the following is an expression for the value of x in terms of y?

1. (4/5)y 2. (2/3)y 3. (3/2)y^2 4. 6y 5. 36y^2

This I had no idea how to do.

Thanks for any help. Please show steps if possible.

Answer 1

For the first question:

I keep needing to use an extra term Z (original # tapes)

10X + Z = [5Y + 1]Z

10X + Z = 5YZ + Z

10X = 5YZ

2X = YZ (I'm not certain this is right either; maybe #5?)

For the second question: [X = variable x = times]

X^9 = 4 & X^7 = 9/Y^2 For the second eq. multiply both sides by Y^2 to give:

X^9 = 4; X^7 x Y^2 = 9 Set them so they're equal

X^7 x Y^2 = [9/4] X^9 pull out the common factor X^7

Y^2 = [9/4] X^2 multiply by reciprocal and rearrange

X^2 = [4/9] Y^2 take square root

X = [2/3] Y answer # 2