PS problems help solve pleaseee

[Immy]

hey...
I need a bit of help on these questions.. .I keep on making an error and I dont see where...
2^(x+y)^2 / 2^(x-y)^2

xy=1

At a speed of 50 mph, a certain car uses 1 gall on of gasoline every 30 miles. if the car starts with a full 12 gallon tank of gasoline and travels for 5 hrs at 50 mph ,the amount of gasoline used would be what fraction of a full tank..

I solved to find the total distance and then just divided 30 miles into the total distance and then took that over the full tank ...


According to the directions on a can of frozen orange juice concertrate, 1 can of concertrate is to be mixed with 3 cans of water to make orange juice. How many 12-ounce cans of the concetrate are required to prepare 200 6-ounce servings of orange juice?

This is a ratio quesiton so i have 1:3 and then i have x over 200? and then cross multiply ? is that right ?

thanks for your help...

[mike22629]

First question:

Use exponent of exponent law

(2^((x+y)^2))/(2^((x- y)^2)=

2^(x^2 + 2xy + y^2) / 2^(x^2 - 2xy + y^2)

Since xy= 1

Top is 4 greater than bottom because both sides have x^2 + y^2, but the top side has (2) and the bottom side has (-2) which is a difference of 4.

2^4 = 16

I believe that the answer is 16.


Second Question

Find out how many gallons are used every 50 miles to find out how many gallons are used per hour (because it takes 1 hour to drive 50 miles at 50 mph)

30x = 50
x=5/3
So 5/3 gallons used per hour.

Multiply by 5 hours

5*(5/3) = 25/3 gallons used in 5 hours at 50 mph.

(25/3)/12

Answer should be 25/36


Question 3.

Ratio is 1:3

Asking to make 1200 ounces of oj (6*200)

1200 ounces of oj requires 300 ounces of concentrate (use ratio of 1:3)

300/12 (amount in each can) =

Answer should be 25.

[Immy]

in question 3 : how do you manage to get 300?

[mike22629]

ratio of 1:3

1/3 = 300/900

300+900= 1200 (total of oj ounces)