Mixture problems

The Mixture problems are part of the algebra word problems. The mixture problems deals with two or more things mixed in different ratio and ask to find price, percentage and some other quantities. For solving mixture problems we need to know the following things,
The total amount = amount of first mixture + amount of second mixture .This formula used to find the unknown mixture amount.
We can form the equation to find unknown value by using the following formula,
(Cheaper value / dearer value) = (mean value –cheaper value)/ (dearer value –mean value)
Let us understand this with the following example on mixture problem.
f Real gold is 92.5% pure gold. How many pounds of Real Gold needs to be mixed to a 90% Gold alloy to obtain a 500g of 91% gold alloy?
Solution:
Let us take x and y be the weights of real gold and of the 90% alloy to make the 500 pounds at 91%.
That is x + y =500
The formula is,
amount₁ (%) + amount₂ (%) = (amount₁ + amount₂) (%)

92.5 % of x + 90% of y = 91% of 500
Substitute y = (500 – x) in the above equation,
We get,
92.5% of x + 90% of (500 - x) = 91% of 500
(92.5x)/100 + (90(500-x))/100 = (91(500))/100
Multiply by 100 on both sides,
92.5x+ 45000-90x=45500
Subtract 45000 on both sides,
92.5x-90x=45500-45000
2.5x=500
Divide by 2.5 on both sides,
X = 500/2.5
X = 200
Answer : 200 pounds of gold needs to make 91% of gold alloy.