Mixture Problem

$x$ = weight of lead in the alloy

$y$ = weight of nickel in the alloy

$one$ $pound$ $=$ $16$ $ounces$

$x+y = 32$

$y = 32 - x$ ----equation (1)

$\frac{10}{11}$ $x +$ $\frac{8}{9}$ $y =$ $28.8$ --- equation (2)

Substitute equation (1) in equation (2)

$\frac{10}{11}$ $x + \frac{8}{9}$ $(32 - x) = 28.8$

$\frac{10}{11}$ $x$ $+$ $\frac{256}{9}$ – $\frac{8}{9}$ $x$ $= 28.8$

$x = 17.6$ $ounces$