Smart Mathematicians i need your help.?

Question

I can't find the square root symbol of X, so i represented it with "square root".
1,Saying that 4< square root X < 9 is equivalent to saying what about X?

2, If the total cost X apples is b cents, what is a general formula for the cost, in cents, of y apples?

Answer 1

1. Square everything in the first set of inequalities.

If 4 < sqrt(x) < 9, then 4^2 < [sqrt(x)]^2 < 9^2

or, 16 < x < 81.

As a test, let's choose x = 64. I picked it because it has an easy square root.

If x = 64 (and note that 16 < 64 < 81), then sqrt(x) = 8, which is greater than 4 and less than 9.

2. If the total cost of x apples is b cents, then the cost of 1 apple is b/x cents. x * b/x = b, which is indeed the cost of x apples according to the problem.

If 1 apple costs b/x cents, then y apples cost yb/x cents.

As a test, suppose that 5 apples cost 20 cents. (That is, x = 5, b = 20). In this case, 1 apple costs 4 cents.

How much are 6 apples (Let's let y = 6). 6 apples would cost 24 cents.

Now, what is yb/x?

6*20/5 = 120/5 = 24.

In this case, it checks out. (It will for all cases, but one case doesn't actually prove that it works. It really only justifies it. But it is right :D)

Answer 2

Since sqrt(X)>4, square both sides to get X>16. Similarly, sqrt(X)<9, so X<81. So 16
How much does 1 apple cost? b/X cents. So Y apples cost bY/X cents.

Answer 3

2 < x < 3.
c = y(x/b).