Answer
2.5 pounds of Kenyan and 0.5 pounds of Sri Lankan went into the mixture.
Work Step by Step
Let's assume that $x$ pounds of Kenyan coffee and $y$ pounds of Sri Lankan coffee had been purchased. As total purchase was $3$ lb i.e. $3$ pounds, Therefore-
$x+y$ = $3$ __eq.1
Now price for one pound of Kenyan is $ 3.50$ dollars and price for one pound of Sri Lankan is $ 5.60$ dollars, and total cost was $11.55$ dollars. Therefore-
$3.5 \times x +5.6 \times y$ = $11.55$
i.e. $3.5 x +5.6 y$ = $11.55$ __eq.2
Substituting for $x$ in eq.2 from eq.1-
$3.5 (3-y) +5.6 y$ = $11.55$
i.e. $10.5 - 3.5y + 5.6 y$ = $11.55$
i.e. $10.5+ 2.1 y$ = $11.55$
i.e. $2.1 y$ = $11.55-10.5$ = $1.05$
i.e. $y$ = $\frac{1.05}{2.1}$ = $0.5$
Substituting for $y$ in eq.1-
$x+0.5$ = $3$
i.e. $x$ = $3-0.5$ = $2.5$
Thus 2.5 pounds of Kenyan and 0.5 pounds of Sri Lankan went into the mixture.
