The sum of two integers is 74. The larger is 13 less than twice the smaller. Find the two integers.
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Let's call the smaller integer x and the larger integer y.
According to the problem, the sum of the two integers is 74, so we can write the equation:
x + y = 74
We are also given that the larger integer is 13 less than twice the smaller integer, therefore we can write another equation:
y = 2x - 13
Now we have a system of two equations. We can solve it by substitution or elimination.
Using the substitution method, we can substitute the value of y in the first equation with its value from the second equation:
x + (2x - 13) = 74
3x - 13 = 74
3x = 74 + 13
3x = 87
x = 87/3
x = 29
Now that we have the value of x, we can substitute it into any of the original equations to find the value of y. Let's use the second equation:
y = 2x - 13
y = 2(29) - 13
y = 58 - 13
y = 45
So the two integers are 29 and 45.
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