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Complete Question
Write a rational equation that relates the desired percentage p, to the amount A of a 30% solution that needs to be added to 1 liter of 10% acid solution to make a blend that is p% acid, where 0<p<100 . What is a reasonable restriction on the set of possible values of ? Explain your answer.
Answer:
100(0.1 + 0.3A)= (1 + A) P
Explanation:
A of a 30% solution that needs to be added to 1 liter of 10% acid solution to make a blend that is p% acid,
Hence,
10% of 1 + 30% of A = p%(1 + A)
0.10 + 0.3A = (p/100)(1 + A)
Divide both sides by 1 + A
0.1 + 0.3A/ 1 + A = p/100
Cross Multiply
100(0.1 + 0.3A) = 1 + A(p)
From the above calculation, we can see that, the blend that would be formed is not lower than 10% or greater than 30%
10% < p< 30%