Question 1088063
Let {{{x}}} be the number of gallons with a 10% alcohol
Let {{{y}}} be the number of gallons with a 15% alcohol
A bartender needs to make 5 gallons of a mixed drink => {{{x+y=5}}}
a mixed drink contains 12% alcohol => {{{0.10x+0.15y=0.12*5}}}
The system of equations
{{{system(x+y=5, 0.10x+0.15y=0.6)}}}
Multiply the second equation by 10
{{{system(x+y=5, x+1.5y=6)}}}
{{{system(x=5-y, x+1.5y=6)}}}
substitute {{{x=5-y}}} into the second equation
{{{system(x=5-y, 5-y+1.5y=6)}}}
{{{system(x=5-y, 0.5y=1)}}}
{{{system(x=5-y, y=2)}}}
{{{system(x=5-2, y=2)}}}
{{{system(x=3, y=2)}}}
A bartender needs to combine 3 gallons with a 10% alcohol and 2 gallons with a 15% alcohol