how many pounds of candy worth $12 per pound should be mixed with candy costing $19 per pound to produce a 70 pound mixture that sells for $15 per pound?
Accepted Solution
A:
Answer:40 poundsStep-by-step explanation:Given: Cost of a candy [tex](c_1)[/tex]= [tex]\$ 12[/tex] per pound Cost of candy [tex](c_2) = \$ 19\ per\ pound[/tex] Total amount of mixture of be produced = [tex]70\ pound[/tex] Selling price of mixture = [tex]\$ 15 \ per\ pound[/tex]Let´s x be the amount of [tex]c_1 [/tex] to be mixed in the mixture.∴ Cost of [tex]c_1[/tex] in the mixture = 12xNext, Cost of [tex]c_2[/tex] in the mixture = [tex](70 - x)\times 19[/tex]And we know the cost of final mixture = [tex]70 \times 15 = 1050[/tex]Now, putting all the value in the equation⇒ [tex]12x + 19 \times (70 - x) = 1050[/tex]⇒ [tex]1330 - 7x = 1050[/tex]⇒ [tex]-7x = -280[/tex]∴ [tex]x = 40\ pound[/tex]∴ 40 pounds of candy worth $12 per pound to be mixed in the mixture.