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If x and y are non-negative integers such that x + 9 = z, y + 1 = z and x + y < z + 5, then the maximum possible value of 2x + y equals
Correct answer is '23'. Can you explain this answer?
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Verified Answer
If x and y are non-negative integers such that x + 9 = z, y + 1 = z an...
Given x + 9 = z = y + 1 and x + y < z + 5
⇒ (z -9)+(z -1) < z +5
⇒ z < 15
Hence the maximum value of z = 14, max of x = 5 and max of y = 13
Required answer, 2 x + y = 2 ´ 5 + 13 = 23
⇒ (z -9)+(z -1) < z +5
⇒ z < 15
Hence the maximum value of z = 14, max of x = 5 and max of y = 13
Required answer, 2 x + y = 2 ´ 5 + 13 = 23
Most Upvoted Answer
If x and y are non-negative integers such that x + 9 = z, y + 1 = z an...
The equation x 9 = z means that x is equal to the value obtained by subtracting 9 from z. Similarly, the equation y 1 = z means that y is equal to the value obtained by subtracting 1 from z.
The equation x y = z represents a binary operation that combines the values of x and y to produce z. However, it is unclear what specific operation is denoted by " " since it is not a recognized mathematical symbol.
If we assume that " " represents addition, then the equation x y = z can be rewritten as x + y = z. In this case, we can substitute the expressions for x and y in terms of z obtained from the first two equations:
(z - 9) + (z - 1) = z
Simplifying this equation, we get:
2z - 10 = z
Subtracting z from both sides, we have:
z - 10 = 0
Adding 10 to both sides, we get:
z = 10
Now that we have determined the value of z, we can substitute it back into the expressions for x and y:
x = z - 9 = 10 - 9 = 1
y = z - 1 = 10 - 1 = 9
Therefore, if the binary operation represented by " " is addition, then the non-negative integer values of x and y that satisfy the given equations are x = 1 and y = 9.
The equation x y = z represents a binary operation that combines the values of x and y to produce z. However, it is unclear what specific operation is denoted by " " since it is not a recognized mathematical symbol.
If we assume that " " represents addition, then the equation x y = z can be rewritten as x + y = z. In this case, we can substitute the expressions for x and y in terms of z obtained from the first two equations:
(z - 9) + (z - 1) = z
Simplifying this equation, we get:
2z - 10 = z
Subtracting z from both sides, we have:
z - 10 = 0
Adding 10 to both sides, we get:
z = 10
Now that we have determined the value of z, we can substitute it back into the expressions for x and y:
x = z - 9 = 10 - 9 = 1
y = z - 1 = 10 - 1 = 9
Therefore, if the binary operation represented by " " is addition, then the non-negative integer values of x and y that satisfy the given equations are x = 1 and y = 9.
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If x and y are non-negative integers such that x + 9 = z, y + 1 = z and x + y < z + 5, then the maximum possible value of 2x + y equalsCorrect answer is '23'. Can you explain this answer?
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