Question 167440
Lex x=amount of pure orange juice that needs to be added
Now we know that the amount of pure orange juice in the 5 qts (0.10*5) plus the amount of pure orange juice added (x) has to equal the amount of pure orange juice in the final mixture (0.40(5+x)), so our equation to solve is:
0.10*5+x=0.40(5+x)  get rid of parens and simplify
0.5+x=2+0.4x  subtract 0.4x and also 0.5 from each side
0.5-0.5+x-0.4x=2-0.5+0.4x-0.4x  collect like terms
0.60x=1.5  divide each side by 0.6
x=2.5 qts-----------------------------amount of pure orange juice needed

CK
0.10*5+2.5=0.40(5+2.5)
0.5+2.5=2+1
3=3

Hope this helps---ptaylor