Question

Question #557ac

Answer 1

`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`

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`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.

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`

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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`

Answer 2

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,