SPLTV SMA Global Prestasi ( Rachelle Raine X-SC 1)
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This document solves a system of linear equations to determine the price of school supplies. It shows: 1) Ali bought 3 books, 1 pen, 2 pencils for Rp 11,000 2) Budi bought 2 books, 3 pens, 1 pencil for Rp 14,000 3) Cici bought 1 book, 2 pens, 3 pencils for Rp 11,000 It sets up equations and eliminates variables to find the price of each item is books = Rp 2,000, pens = Rp 3,000, pencils = Rp 1,000. Finally, it calculates that Dedi would pay Rp 8,000 for 2 books, 1 pen,
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4. The third solution considers the probability of picking each number on a given pick, integrating to again show the expected number of picks is e.
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SPLTV SMA Global Prestasi ( Rachelle Raine X-SC 1)
- 1. R A C H E L L E R A I N E A G N E T H A V O L A R E A N D E R S
- 3. Ali = 3 buku tulis, 1 pena, 2 pensil = Rp 11.000,00 3x + y + 2z = 11.000 … ( 1 ) Budi = 2 buku tulis, 3 pena, 1 pensil = Rp 14.000,00 2x + 3y + z = 14.000 … ( 2 ) Cici = 1 buku tulis, 2 pena, 3 pensil = Rp 11.000,00 x + 2y + 3z = 11.000 … ( 3 ) “x” stands for books. “y” stands for pens. “z” stands for pencil.
- 4. ①Calculate ( 1 ) and ( 2 ) 3x + y + 2z = 11.000 | x2 | 6x + 2y + 4z = 22.000 2x + 3y + z = 14.000 | x3 | 6x + 9y + 3z = 42.000 - -7y + z = -20.000 … ( 4 ) It depends on us which variables we want to get rid of. In this case, I chose “x” In order to get rid of “x”, we need to make both statements the same. That is why it is times by 2 and 3. This way, we can get rid of “x” This fourth statement, will help us in finding either “y” or “z”
- 5. ②Calculate ( 2 ) and ( 3 ) 2x + 3y + z = 14.000 | x1 | 2x + 3y + z = 14.000 x + 2y + 3z = 11.000 | x2 | 2x + 4y + 6z = 22.000 – -y – 5z = -8.000 … ( 5 ) Since in the first calculation we chose to get rid of “x”, we must get rid of “x” as well in this particular calculation. We do the same step like we did before in the first calculation. Same as the fourth statement, the fifth statement will help us in finding either “y” or “z”
- 6. ③Calculate ( 4 ) and ( 5 ) -y – 5z = -8.000 | x7 | -7y – 35z = -56.000 -7y + z = -20.000 | x1 | -7y + z = -20.000 – -36z = -36.000 z = 1.000 After we have used the first, second, and third statement, now we can use the fourth and the fifth to find either “y” or “z” It is completely up to us to find “y” or “z” first, but in this matter I chose to find “z” first. Same as before, we times both statements to get rid of “y” in order to find the result of “z”
- 7. Find the result of y -7y + z = -20.000 -7y + 1.000 = -20.000 -7y = -20.000 – 1.000 -7y = -21.000 y = 3.000 Since we have found the result of “z”, we can now find the result of “y” by choosing either from the fourth and fifth statement. Since we have found the result of “z”, we can put it this way in order to find “y”
- 8. Find the result of x x + 2y + 3z = 11.000 x + 2(3.000) + 3(1.000) = 11.000 x + 6.000 + 3.000 = 11.000 x = 11.000 – 6.000 – 3.000 x = 2.000 After we have found “y” and “z”, it is now possible for us to find “x” To find “x”, we need to use either the first, the second, or the third statement since we have known both “y” and “z”
- 9. “Dedi membeli 2 buku tulis, 1 pena, dan 1 pensil.” Using the statement written above, we can conclude that : 2(2.000) + 3.000 + 1.000 = 8.000 So, Dedi needs to pay for Rp 8.000,00. Since the amount of books being bought by Dedi are two, so we need to times 2. Using the rule before in Step 1 : x = book y = pen z = pencil It is the same as, 2x + y + z = 8.000 (using variables)