How many cashews at $$ 1.58$ per pound must be mixed with walnuts that cost $78$ cents per pound to make a mixture of $40$ pounds of nuts that cost $$ 1.50$ per pound?

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Solution

Step-1: Cost of cashews:
Let, $x$ be the number of pounds of cashews in the mixture.
Cost of $1$ pound cashew = $$ 1.58$ per pound.
Cost of $x$ pounds cashew = $x$ . $$ 1.58$
Step-2: Cost of Walnuts:
Total number of pounds of nuts $=$ $40$ pounds
So,
number of pounds of walnuts $=$ $40 - x$
Cost of $1$ walnut $=$ $78$ cents per pound.
$1$ cent $=$ $$ 0.01$
$78$ cents $=$ $$ 0.78$
Cost of $40 - x$ walnuts $=$ $(40 - x)$ . $$ 0.78$
Step-3: Find the pounds of cashews.
Cost of $1$ pounds of nuts is $$ 1.50$ per pound
Cost of $40$ pounds of nuts is $40 ($ 1.50)$
$Cost of 40 pounds of nuts = Cost of x pounds cashew + Cost of (40 - x) pounds walnuts$
So,
$\begin{array}{rcl} 40 (1.50) & = & x (1.58) + (40 - x) (0.78) \\ 28.8 & = & 0.8 x \\ x & = & 36 \end{array}$
Hence, the number of pounds of cashews is $36$ .

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How many cashews at $1.58 per pound must be mixed with walnuts that cost 78 cents per pound to make a mixture of 40 pounds of nuts that cost $1.50 per pound?

How many cashews at $$ 1.58$ per pound must be mixed with walnuts that cost $78$ cents per pound to make a mixture of $40$ pounds of nuts that cost $$ 1.50$ per pound?