# Question #93e34

Jul 10, 2016

cashews$= 35$ lb
hazelnuts $= 15$ lb

#### Explanation:

Since we are required to find two quantities, we have two unknowns and need to formulate two equations.

Let us mix with 50 lbs of peanuts cashews $= x$ lb
And let us mix with 50 lbs of peanuts hazelnuts$= y$ lb
Total mixture$= 100$ lb

This gives us first equation
$x + y + 50 = 100$
$x + y = 50$ .....(1)

Cost of $x$ lb of cashews$= 3.00 \times x = 3 x$
Cost of $y$ lb of hazelnuts$= 2.50 \times y = 2.5 y$
Cost of 50 lbs of peanuts$= 1.75 \times 50 = 87.5$
Total cost of mixture$= 3 x + 2.5 y + 87.5$
Per lb cost of mixture gives us the second equation
$\frac{3 x + 2.5 y + 87.5}{100} = 2.30$
To eliminate decimals multiplying both sides by $1000$ we get

$30 x + 25 y + 875 = 2300$
$\implies 30 x + 25 y = 1425$ .......(2)

To solve the set of equation. From (1) we obtain
$x = 50 - y$,
inserting in (2) we get
$30 \left(50 - y\right) + 25 y = 1425$
$1500 - 30 y + 25 y = 1425$
$- 5 y = - 75$
$\implies y = 15$
This gives us
$x = 50 - y = 50 - 15 = 35$