the sum of 2 integers is 41.when 3 times the smaller is subtracted from the larger the result is 17. find 2 integers
just put the words into math:
x+y = 41
y - 3x = 17
Since y=3x+17,
x + 3x+17 = 41
x = 6
so, y = 35
When an integer is subtracted from 6 times the next consecutive integer, the difference is 41. Find the value of the greater integer.
When an integer is subtracted from 3 times the next consecutive integer, the difference is 23. Find the value of the lesser integer.
To solve this problem, we'll need to set up a system of equations based on the information given.
Let's assume the smaller integer is "x" and the larger integer is "y".
From the first statement, we know that the sum of the two integers is 41. So, we can write the equation: x + y = 41. (Equation 1)
From the second statement, we know that when 3 times the smaller integer is subtracted from the larger integer, the result is 17. So, we can write the equation: y - 3x = 17. (Equation 2)
Now we have a system of two equations with two unknowns. We can solve this system using substitution or elimination.
Let's use substitution to solve the system:
We can solve Equation 1 for x in terms of y by subtracting y from both sides: x = 41 - y.
Now, substitute this value of x into Equation 2:
y - 3(41 - y) = 17.
Simplify the equation: y - 123 + 3y = 17.
Combine like terms: 4y - 123 = 17.
Add 123 to both sides: 4y = 140.
Divide by 4: y = 35.
Now, substitute this value of y back into Equation 1 to find x:
x + 35 = 41.
Subtract 35 from both sides: x = 6.
So, the two integers are 6 and 35.