Quandaries
and Queries 

Cashews are sold for 1.20 per 1/4 pound and Brazil nuts are sold for $1.50 per 1/4 pound. If you mix 20lbs of Brazil nuts, how many cahsews would it take to make a mix that sells for $1.30 per 1/4 pound? Give me the equation that gives the answer 

Hi Bob, Since you are told the number pounds of Brazil nuts in the final mixture I would first change the prices from dollars per quarter pound to dollars per pound. The question then becomes
The 20 pounds of Brazil nuts in the final mixture cost
You don't know the number of pounds of cashews in the final mixture so create a variable for it. Let x be the number of pounds of cashews in the final mixture. Cashews cost $4.80 per pound so these x pounds cost
The final mixture then has 20 + x pounds of nuts worth $5.20 per pound so the final mixture is worth
The final mixture is made up of the Brazil nuts and the cashews so the cost of the final mixture must be the sum of the costs of the two components. Thus
Penny 

