Answer :
5 gallons of 50 % alcohol solution is used
Solution:
Let "x" is the gallons of 50 % alcohol solution
Then, 10 gallons is 35 % solution
The, 10 + x is the gallons of 40 % solution
Then, according to question,
"x" gallons of 50 % solution is mixed with 10 gallons of 35 % solution to get 10 + x gallons of 40 % solution
Therefore,
[tex]50 \% \times x + 35 \% \times 10 = 40 \% \times (10+x)\\\\\frac{50}{100} \times x + \frac{35}{100} \times 10 = \frac{40}{100} \times 10+x\\\\0.5x + 3.5 = 0.4(10+x)\\\\0.5x + 3.5=4+0.4x\\\\0.5x-0.4x = 4-3.5\\\\0.1x = 0.5\\\\Divide\ both\ sides\ by\ 0.1\\\\x = 5[/tex]
Thus 5 gallons of 50 % alcohol solution is used