Question

Seorang penjual beras mencampur 3 jenis beras. campuran pertama terdiri atas 1 kg jenis a , 2 kg jenis b , dan 4 kg jenis c dijual dengan harga Rp.19.500 . campuran beras kedua terdiri dari 2 kg jenis a dan 3 kg jenis b dijual harga Rp.19.000 . campuran beras ketiga terdiri atas 1 kg jenis b dan 1 kg jenis c dijual dengan harg Rp.6.250 . harga beras jenis manakah yang paling mahal

Answer 1

Translation to English:

A rice supplier mixes three different types of rice into three different blends; Type A, Type B, and Type C.

He blends 1 kg of type A, 2 kg of type B, and 4 kg of type C and sells the blend for IDR 19500
He also blends 2 kg of type A and 3 kg of type B and sells the blend for IDR 19000
The third blend consists of 1 kg of type B and 1 kg of type C and this blend is sold for IDR 6250

Which type of rice is the most expensive?

Solution:

Start with the third blend:
1 kg of type B + 1 kg of type C = 6250
B + C = 6250
B = 6250 - C

Then move on to the second blend:
2 kg of type A + 3 kg of type B = 19000
2A + 3B = 19000
2A + 3(6250 - C) = 19000
2A + 18750 - 3C = 19000
2A - 3C = 19000 - 18750
2A - 3C = 250
2A = 250 + 3C
A = [250 + 3C] / 2

Then move on to the first blend:
1 kg of type A + 2 kg of type B + 4 kg of type C = 19500
A + 2B + 4C = 19500
$\frac{250+3C}{2}+2(6250-C)+4C=19500$ ⇒ Multiply each term by 2
$(250+3C)+4(6250-C)+8C=39000$
$250+3C+25000-4C+8C=39000$
$25250+7C=39000$
$7C=39000-25250$
$7C = 13750$
$C=1964.3$

B + C = 6250
B + 1964.3 = 6250
B = 6250 - 1964.3
B = 4285.7

A = [250+C] /2
A = [250 + 1964.3] / 2
A = 1107.15

The most expensive rice is type B

Answer 2

The type of rice which is most expensive is $\boxed{\text{\bf type B}}$.

Further details:

It is given that the rice seller mixes three types of rice and the total number of mixture is three.

The first mixture consists $1\text{ kg}$ rice of type $\text{A}$, $2\text{ kg}$ rice of type $\text{B}$ and $4\text{ kg}$ rice of type $\text{C}$.

The selling price of the first mixture is $19500$.

In equation form it can be written as follows:

$\boxed{\text{A}+2\text{B}+4\text{C}=19500}$      .......(1)

The second mixture consists $2\text{ kg}$ rice of type $\text{A}$ and $3\text{ kg}$ rice of type $\text{B}$.

The selling price of the second mixture is $19000$.

In equation form it can be written as follows:

$\boxed{2\text{A}+3\text{B}=19000}$   ......(2)

The third mixture consists $1\text{ kg}$ rice of type $\text{B}$ and $1\text{ kg}$ rice of type $\text{C}$.

The selling price of the third mixture is $6250$.

In equation form it can be written as follows:

$\boxed{\text{B}+\text{C}=6250}$ ........(3)

Rearrange the equation (3) to obtain the value of $\text{B}$ as follows:

$\text{B}=6250-\text{C}$            ...........(4)

Substitute this value of $\text{B}$ in equation (2).

$\begin{aligned}2\text{A}+3(6250-\text{C})&=19000\\2A+(3\cdot 6250)-3\text{C}&=19000\\2\text{A}-3\text{C}+18750&=19000\\2\text{A}-3\text{C}&=19000-18750\\2\text{A}-3\text{C}&=250\end{aligned}$  

Further solve the above equation,

$\text{A}-1.5\text{C}=125$   ......(5)

Now substitute the value of $\text{B}$ from equation (4) in equation (1) to obtain an equation in the form of $\text{A}$ and $\text{C}$ as follows,

$\begin{aligned}\text{A}+2(6250-\text{C})+4\text{C}&=19500\\ \text{A}+(2\cdot 6250)-2\text{C}+4\text{C}&=19500\\ \text{A}+12500+2\text{C}&=19500\\ \tex{A}+2\text{C}&=19500-12500\end{aligned}$

Further the above equation can be simplifies as follows,

$\text{A}+2\text{C}=7000$            .......(6)

Subtract the equation (4) from (5) to obtain the value of $\text{A}$ and $\text{C}$.  

$\begin{aligned}\text{A}+2\text{C}-\text{A}+1.5\text{C}&=7000-125\\3.5\text{C}&=6875\\ \text{C}&=1964.3\end{aligned}$

Substitute this value of $\text{C}$ in equation (5) to obtain the value of $\text{A}$ as follows,

$\begin{aligned}\text{A}+(2\cdot 1964.3)&=7000\\ \text{A}&=7000-3928.6\\ \text{A}&=3071.4\end{aligned}$

Again substitute $\text{C}=1964.3$ in equation (4) to obtain the value of $\text{B}$.

$\begin{aligned}\text{B}&=6250-1964.3\\&=4285.7\end{aligned}$  

Therefore, the most expensive type of rice is $\boxed{\text{\bf type B}}$.

Learn more:

1.  Problem on percentage in a survey: brainly.com/question/3724002

2. Problem on unit conversion factor: brainly.com/question/5009365

3. Problem on to find the value in pounds: brainly.com/question/4837736

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Mixtures

Keywords:  Rice seller, mixture, sold, expensive, type A, type B, type C, simplification, consist, 19500, 1 kg,addition, substitution, multiplication.