Question 342037
The 5 pounds of mixed nuts cost $30, not $30/LB.  So the total mixture of  50# needs to cost 50LB * $2.90/LB = $145.  The 5LB of mixed nuts cost $30, so the remaining 45LB need to cost $115.  Peanuts + Cashews = 45LB, or P + C = 45.  $1.50P + $4.50C = $115.  Standard two equations in two unknowns.  Solve the first equation for C, C= 45 - P, and substitute into the second equation, so 
$1.50P + $4.50(45 - P) = $115
$1.50P + $202.50 - $4.50P = $115
$202.50 - $3.00P = $115
$3.00P = $87.50
P = 29.16667 LB
C = 45 - 29.16667 = 15.83333
Checking - 29.16667($1.50) + 15.83333($4.50) = $115