Avegetable stand sells watermelons $5 each and honeydew melons for $3 each. one day they sold 6 more honeydew melons than watermelons, and their sales totaled $98.write andsolve a system of equations to find how many watermelons and honeydew melons they sold

step-by-step explanation:

consider the statement as given in the text book,

let    be the number of acre of watermelon and    be the number of acre of cantaloupes.

number of salable units from each acre planted with watermelon is 90.

the selling price of a water melon is  

therefore, selling price of 90 watermelons is



total money that farmer will earn from    number of acres of watermelon is.

every acre of watermelon requires 20 pounds of fertilizer.

the cost price of 50-pound bag of fertilizer is  

cost price of 1-pound bag of fertilizer is  

cost price of 20-pound bag of fertilizer is



cost price of 20-pound bag of fertilizer for    be the acre of watermelon is  

the cost price of 1 hour of labor is  

the cost price of 2 hour of labor is



the cost price of 2 hour of labor is for    acre of watermelon is  

therefore, profit earned by farmer from watermelon is



number of salable units from each acre planted with cantaloupes is 300.

the selling price of cantaloupes is  

therefore, selling price of 300 cantaloupes is



total money that farmer will earn from    number of acres of cantaloupes is.

every acre of cantaloupes requires 15 pounds of fertilizer.

the cost price of 50-pound bag of fertilizer is  

cost price of 1-pound bag of fertilizer is  

cost price of 15-pound bag of fertilizer is



cost price of 15-pound bag of fertilizer for    be the acre of cantaloupes is  

the cost price of 1 hour of labor is  

the cost price of 2.5 hour of labor is



the cost price of 2.5 hour of labor is for    acre of cantaloupes is  

therefore, profit earned by farmer from cantaloupes is



the farmer wants to maximize their profit. therefore, the objective function for this model will be,

max:   

as farmer has 100-acre of farm with him. therefore,



as every acre planted with watermelon requires 50 gallons of water, so  acre planted with watermelon will require    gallons of water.

as every acre planted with cantaloupes require 75 gallons of water, so  acre planted with cantaloupes will require    gallons of water.

as farmer can pump about 6000 gallons of water, therefore



hence,  the lp mode for this model is shown below,

max:   

subject to:



x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

good luck on your studies! : )

david edward.