The weight of apples is: 100 The weight of pairs is: 65
Let the mass in pounds of apples be##” ” a## Let the mass in pounds of pairs be ##” “p##
Let total income from apples be ##” “T_a##
Let the total income from pairs be ##” “T_p##
##color(blue)(“Breaking the question into parts to build the equations:”)##
Sold a total of 165 pound of apples##” “->a+p=165## ….(1)
Sold apples for $1.75 per pound ##” “-> T_a=1.75xxa##….(2) Sold pairs for $2.50 per pound##” “->T_p=pxx2.50##….(3)
She made $337.50 ##” “->T_a+T_p=337.50##…..(4) ‘~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
##color(blue)(“Determine the value of p”)##
From equation (1) ##color(brown)(a=165-p” “……….(1_a))##
Substituting equations (2) and (3) into (4)
##T_a+T_p=337.50″ “->” “1.75color(green)(a)+2.5p=337.50##
But from ##(1_a) ” “color(green)(a)=165-p## giving
##T_a+T_p=337.50″ “->” “1.75(color(green)(165-p))+2.5p=337.50##
##288.75-1.75p+2.5p=337.5##
##288.75 +0.75p=337.5##
##p=(337.5-288.75)/(0.75)##
##color(red)(p= 65)##…………………………………(5) ‘~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ##color(blue)(“Determine the value of a”)##
Substitute equation (5) into equation (1)
##a+color(green)(p)=165″ “->” “a+color(green)(65)=165##
##a=165-65 = 100##
##color(red)(a=100)## .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Check: ##$1.75(100) + $2.50(65)” “=” “$175+$162.5” “=” “$337.5 ” “-> color(red)(“True”)##
