if I add 1 to each of the two given numbers then their ratio is 1:2. If I subtract 5 from each of the numbers, the ratio is 5:11. Find the numbers by elimination meth.
Answers
Let the two numbers be X and Y.
1 is added to each Number then the numbers becomes X+1 and Y+1
According to question,
X + 1/Y+1 = 1/2
2(X+1) = 1(Y+1)
2X + 2 = Y +1
2X -Y = 1-2
2X - Y = -1---------(1)
5 is subtracted to each NUMBERS then the numbers becomes (X-5) and (Y-5).
According to question,
(X-5)/(Y-5) = 5/11
11(X-5) = 5(Y-5)
11X - 55 = 5Y - 25
11X - 5Y = -25+55
11X - 5Y = 30---------(2)
From equation (1) we get,
2X - Y = -1
2X = -1 + Y
X = -1+Y/2--------(3)
Putting the value of X in equation (2)
11X - 5Y = 30
11 × (-1+Y/2) - 5Y = 30
-11 + 11Y/2 - 5Y = 30
-11+11Y - 10Y = 30 × 2
Y - 11 = 60
Y = 60+11
Y = 71
Putting the value of Y in equation (3)
X = -1+Y/2 => -1 + 71/2 => 70/2
X = 35
Hence,
Number are 71 and 35.
HOPE IT WILL HELP YOU...... :-)
Answer:
The number are 71 and 35.
Step-by-step explanation:
Let the two numbers be X and Y.
1 is added to each Number then the numbers become X+1 and Y+1
According to the question,
Step 1
X + 1/Y+1 = 1/2
2(X+1) = 1(Y+1)
2X + 2 = Y +1
2X -Y = 1-2
2X - Y = -1---------(1)
5 is subtracted from each number then the numbers become (X-5) and (Y-5).
According to the question
Step 2
(X-5)/(Y-5) = 5/11
11(X-5) = 5(Y-5)
11X - 55 = 5Y - 2
11X - 5Y = -25+5
11X - 5Y = 30---------(2
From equation (1) we get,
2X - Y = -
2X = -1 + Y
X = -1+Y/2--------(3)
Putting the value of X in equation (2)
Step 3
11X - 5Y = 30
11 × (-1+Y/2) - 5Y = 30
-11 + 11Y/2 - 5Y = 30
-11+11Y - 10Y = 30 × 2
Y - 11 = 60
Y = 60+11
Y = 71
Step 3
Putting the value of Y in equation (3)
X = -1+Y/2 => -1 + 71/2 => 70/2
X = 35
Hence,
The number are 71 and 35.
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