nick1272
Answered

Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Join our platform to connect with experts ready to provide detailed answers to your questions in various areas. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

Please explain how to solve this problem

A nut store normally sells cashews for​ $4.00 per pound and peanuts for​ $1.50 per pound. But at the end of the month the peanuts had not sold​ well, so, in order to sell 80 pounds of​ peanuts, the manager decided to mix the 80 pounds of peanuts with some cashews and sell the mixture for $2.00 per pound. How many pounds of cashews should be mixed with the peanuts to ensure no change in the​ revenue?

The manager should mix _ pounds of cashews with the peanuts.

Sagot :

sqdancefan

9514 1404 393

Answer:

  20 pounds

Step-by-step explanation:

Often, mixture problems are worked by writing two equations: one for the total quantity of constituents in the mix, and one for the total price of the mix. When these equations are solved by substitution, the first step is to write one quantity in terms of the other.

You can save an equation and a step by using one variable for quantity. It usually works best to let the variable represent the highest-cost (or most concentrated) contributor. Here, that is the quantity the problem asks for, so ...

Let c represent the number of pounds of cashews needed to be mixed with the peanuts. Then the revenue from selling the mix is ...

  80($1.50) +c($4.00) = (80+c)($2.00)

  120 +4c = 160 +2c . . . . . divide by $, simplify

  2c = 40 . . . . . . . . . . . . . subtract 120+2c from both sides

  c = 20 . . . . . . . . . . . . . divide by 2

The manager should mix 20 pounds of cashews with the 80 pounds of peanuts.

We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.