The scale on a map reads 3⁄4 inches = 60 miles. If two cities are 2 1⁄2 inches apart on the map, find the actual distance betwee
1 answer:
You might be interested in
Given:
A solution of 60% fertilizer is to be mixed with a solution of 21% fertilizer to form 234 liters of a 43% solution.
To find:
The quantity of the 60% solution in the mixture.
Solution:
Let x be the quantity of the 60% solution and y be the quantity of the 21% solution.
Quantity of mixture is 234. So,
...(i)
The mixture has 43% fertilizer. So,
Multiply both sides by 100.
...(ii)
Using (i) and (ii), we get
Divide both sides by -39.
Putting this value in (i), we get
Therefore, 132 liters of the 60% solution must be used.
So firstly, you want to multiply both sides by (x-2)(x+2) since it is the LCM, or lowest common multiplier. Your equation will look like this:
Next, you can cancel out the denominators on 3/x+2 and 4/x-2 on the left side:
Next, foil:
Next, combine like terms:
Next, add x + 14 on both sides:
Next, replace x with -5x + 6x:
Next, factor 5x^2-5x and 6x-6 separately. Make sure that both factors have the same quantity within the parentheses:
With this, we can rewrite it as From here, we solve for x in (5x+6) and (x-1) separately and setting them to zero.
In short, x = -1.2, 1.