Math question please help

nbhardwaj wrote:Suppose you like 1% milk, but you have only 3% whole milk and ½% low fat milk. How much of each should you mix together to make an 8 ounce cup of 1% milk?

two ways to solve this problem - by applying equation or alligation methods. Both shown below

equation method
Let's denote a=3% milk and b=0.5% milk, then Equation 1. 0.03a+0.005b=0.01(a+b) and Equation 2. a+b=8 (ounce cup). Solve for a and b
{30a+5b=10a+10b
{a+b=8

{20a=5b, 4a=b
{a+4a=8, a=8/5 and b=32/5

alligation method
The proportion needed of each starting percentage is the positive difference between the other two percentages.

3% <---> 0.5% // 1%
______________// 8

proportion needed for 0.5% milk = 3-1=2
proportion needed for 3% milk = 1-0.5=0.5

0.5% milk/3% milk=2:0.5=4:1

8 ounce cups will make a whole part of ratios or 5 and the other ratios will be 0.5% milk=4/5 and 3% milk=1/5 OR 0.5% milk=(4/5)*8=32/5 and 3% milk=(1/5)*8=8/5

it is a weighted average q., and the formula is -

Low milk/whole milk=(3%-1%)/(1%-1/2%)=4:1

low milk =(4/5)*8=32/5

whole milk=(1/5)*8=8/5

nbhardwaj wrote:Suppose you like 1% milk, but you have only 3% whole milk and ½% low fat milk. How much of each should you mix together to make an 8 ounce cup of 1% milk?

Can anyone elaborate on using the alligation method for this question?