Respuesta :
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
[tex] \frac{250+3C}{2}+2(6250-C)+4C=19500 [/tex] ⇒ Multiply each term by 2
[tex](250+3C)+4(6250-C)+8C=39000[/tex]
[tex]250+3C+25000-4C+8C=39000[/tex]
[tex]25250+7C=39000[/tex]
[tex]7C=39000-25250[/tex]
[tex]7C = 13750[/tex]
[tex]C=1964.3[/tex]
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
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
[tex] \frac{250+3C}{2}+2(6250-C)+4C=19500 [/tex] ⇒ Multiply each term by 2
[tex](250+3C)+4(6250-C)+8C=39000[/tex]
[tex]250+3C+25000-4C+8C=39000[/tex]
[tex]25250+7C=39000[/tex]
[tex]7C=39000-25250[/tex]
[tex]7C = 13750[/tex]
[tex]C=1964.3[/tex]
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
The type of rice which is most expensive is [tex]\boxed{\text{\bf type B}}[/tex].
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 [tex]1\text{ kg}[/tex] rice of type [tex]\text{A}[/tex], [tex]2\text{ kg}[/tex] rice of type [tex]\text{B}[/tex] and [tex]4\text{ kg}[/tex] rice of type [tex]\text{C}[/tex].
The selling price of the first mixture is [tex]19500[/tex].
In equation form it can be written as follows:
[tex]\boxed{\text{A}+2\text{B}+4\text{C}=19500}[/tex] .......(1)
The second mixture consists [tex]2\text{ kg}[/tex] rice of type [tex]\text{A}[/tex] and [tex]3\text{ kg}[/tex] rice of type [tex]\text{B}[/tex].
The selling price of the second mixture is [tex]19000[/tex].
In equation form it can be written as follows:
[tex]\boxed{2\text{A}+3\text{B}=19000}[/tex] ......(2)
The third mixture consists [tex]1\text{ kg}[/tex] rice of type [tex]\text{B}[/tex] and [tex]1\text{ kg}[/tex] rice of type [tex]\text{C}[/tex].
The selling price of the third mixture is [tex]6250[/tex].
In equation form it can be written as follows:
[tex]\boxed{\text{B}+\text{C}=6250}[/tex] ........(3)
Rearrange the equation (3) to obtain the value of [tex]\text{B}[/tex] as follows:
[tex]\text{B}=6250-\text{C}[/tex] ...........(4)
Substitute this value of [tex]\text{B}[/tex] in equation (2).
[tex]\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}[/tex]
Further solve the above equation,
[tex]\text{A}-1.5\text{C}=125[/tex] ......(5)
Now substitute the value of [tex]\text{B}[/tex] from equation (4) in equation (1) to obtain an equation in the form of [tex]\text{A}[/tex] and [tex]\text{C}[/tex] as follows,
[tex]\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}[/tex]
Further the above equation can be simplifies as follows,
[tex]\text{A}+2\text{C}=7000[/tex] .......(6)
Subtract the equation (4) from (5) to obtain the value of [tex]\text{A}[/tex] and [tex]\text{C}[/tex].
[tex]\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}[/tex]
Substitute this value of [tex]\text{C}[/tex] in equation (5) to obtain the value of [tex]\text{A}[/tex] as follows,
[tex]\begin{aligned}\text{A}+(2\cdot 1964.3)&=7000\\ \text{A}&=7000-3928.6\\ \text{A}&=3071.4\end{aligned}[/tex]
Again substitute [tex]\text{C}=1964.3[/tex] in equation (4) to obtain the value of [tex]\text{B}[/tex].
[tex]\begin{aligned}\text{B}&=6250-1964.3\\&=4285.7\end{aligned}[/tex]
Therefore, the most expensive type of rice is [tex]\boxed{\text{\bf type B}}[/tex].
Learn more:
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2. Problem on unit conversion factor: https://brainly.com/question/5009365
3. Problem on to find the value in pounds: https://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.
