How many pounds of gourmet candy selling for $2.20 per pound should be mixed with 6 pounds of gourmet candy selling for $1.20 per pound to obtain a mixture selling for $1.60 per pound?

1 Answer
Feb 5, 2016

Answer:

#color(green)("$1.20 candy amount is "6"lb"#
#color(green)("$2.20 candy amount is "4"lb"#

Explanation:

Tony B

There are two ways of solving this.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Method 1")#

#color(Brown)("Straight line graph approach")#

Standard form equation#" "->y=mx+c#

In this case:#" "c=1.2"; "m=(2.20-1.20)/100 = 1/100"; "y=1.60#

#1.6=x/100+1.2#

#x=(1.6-1.2)xx100" "color(purple)(-> x=0.4xx100)#

#x=40-> 40%#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Method 2")#

#color(Brown)("Ratios, which is the same thing as method 1 just that this fact is in disguise.")#

The approach is based on the principle that the gradient is constant.

#100/(2.2-1.2)=x/(1.6-1.2)#

Basically this is saying that the gradient of the whole is the same gradient as part of it!

#100/1=x/0.4#

#color(purple)(0.4xx100=x)#

#x=40" " -> 40%#

#color(green)('"NOTE THAT IS 40% OF THE $2.20 CANDY")#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine the weights of each constituent")#

so #100%-40% =60%# as the proportion of the $1.20 candy

Let the whole weight be #w# then

#60/100 w=6#

#w=(6xx100)/60" "=" "100/10" "=" "10lb#

So

#color(green)("$1.20 candy amount is "6"lb"#
#color(green)("$2.20 candy amount is "10-6 = 4"lb"#