Question #557ac

2 Answers
Sep 22, 2016

Answer:

#17 1/7" Kg of the P50 rice should be added to 15 Kg of P35 rice"#

#color(red)("The explanation makes this a lot longer than just doing the calculation")#

Explanation:

There are several ways of approaching this problem. I tend to use a method related to a straight line graph equation but just using the gradient. This turns out to be ratios.

#color(blue)("Preamble")#

Let rice type 1 be #R_1->" selling at P50.00 per Kg"#

Let rice type 2 be #R_2->" selling at P15.00 per Kg"#

Let the final weight be #w#

The target blend will cost P35.00

If the mix were to be all #R_1# the cost would be P50
If the mix were to be all #R_2# the cost would be P15

If we have all #R_1# then there is no #R_2#
If we have no #R_1# then it is all #R_2#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Solving the question")#

Using the above information and plot the content of only #R_1# against cost of the mix and we have our model.

Tony B

Using ratio #-> # the gradient of part is the gradient of all

#("change in along")/("change in up") -> 100/(50-35) -=x/(43-35)#

#=>100/15=x/8#

#x=(8xx100)/15 = 53 1/3# but this is percent

#=> R_1 =53 1/3%" of the mix "w#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
If #R_1->53 1/3%# then #R_2->(100-53 1/3)%#

#=> R_2=46 2/3%#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

But we are told that the quantity of #R_2# is fixed at 15 Kg implying that the whole weight #(w)# is such that:

#R_2=(46 2/3)/100 xx w =15#

#=> w=15xx 100/(46 2/3) = 32 1/7" Kg"#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#R_1-> P50.00 "rice"#

Thus the weight of #R_1 = w-15" "=" "32 1/7 -15" " =" " 17 1/7 Kg#

Sep 24, 2016

Answer:

The two types of rice should be mixed in the ratio of #8:7#

Explanation:

We are only concerned with the price per Kilo, not an actual number of Kilograms.

Let's consider a whole kilo, split into two parts:

Whatever part is the first rice, #R_1# the rest will be the second rice #R_2#

Let the amount of #R_1# be x.

Then the amount of #R_2# is #1-x#

The cost of #R_1# is #50x#

The cost of #R_2# is #35(1-x)#

Together the value of the mixture is #43#

#50x+ 35(1-x) = 43#

#50x+35-35x = 43#

#15x = 43-35#

#15x = 8#

#x = 8/15#

#:. 1-x = 7/15#

The two types of rice should be mixed in the ratio of:

Expensive rice : cheaper rice
#8 : 7#

As a check - average the two prices:

#(50+35)/2 = 42.50#

As the required price of P43 is slightly more than P42.50, a ratio of #8:7# seems reasonable,