Two positive numbers differ by 11. When the larger number is divided by the smaller, the quotient is 2 and the remainder is 4. what are the numbers
x = larger number
y = smaller number
Equations:
x - y = 11
x/y = 2 + 4/y
Get rid of fractions in second equation by multiplying by y.
y(x/y = 2 + 4/y)
x = 2y + 4 > plug this into the first equation.
Solve for y and then x.
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To solve this problem, we can set up a system of equations. Let's call the larger number "x" and the smaller number "y".
From the first sentence, we know that the larger number is 11 more than the smaller number. So we can write the equation:
x = y + 11
Next, we're told that when the larger number (x) is divided by the smaller number (y), the quotient (result of the division) is 2 and the remainder is 4. We can write this equation as:
x = 2y + 4
Now we can solve the system of equations by substituting the first equation into the second equation:
(y + 11) = 2y + 4
Simplifying this equation, we get:
y + 11 = 2y + 4
Subtracting y from both sides, we have:
11 = y + 4
Subtracting 4 from both sides, we get:
7 = y
Now that we have the value of y, we can substitute it back into the first equation to find x:
x = y + 11
x = 7 + 11
x = 18
Therefore, the two numbers are 7 and 18.