find 2 integers such that the sum of the greater number and 4 times the lesser number is 156.
Let's represent the two integers as x and y, with x being the greater number.
According to the given condition, we can write the equation:
x + 4y = 156
Now, we need to find two integers that satisfy this equation.
Let's assume x = 30 and y = 36.
30 + 4(36) = 30 + 144 = 174 ≠ 156
This set of numbers does not satisfy the condition.
Let's assume x = 34 and y = 30.
34 + 4(30) = 34 + 120 = 154 ≠ 156
This set of numbers also does not satisfy the condition.
Let's assume x = 40 and y = 29.
40 + 4(29) = 40 + 116 = 156
This set of numbers, x = 40 and y = 29, satisfies the condition where the sum of the greater number and 4 times the lesser number is 156.
Let's assume the two integers are x and y, where x is the greater number and y is the lesser number. According to the given information:
Step 1: Set up the equations:
x + 4y = 156 (Equation 1)
Step 2: Solve for one variable in terms of the other:
Let's solve Equation 1 for x:
x = 156 - 4y
Step 3: Substitute the value of x in terms of y into the other equation:
156 - 4y + 4y = 156
Step 4: Simplify and solve for y:
156 = 156
Since this equation is true, there are infinitely many solutions for y.
Step 5: Choose a value for y and substitute it into the equation for x:
For example, let's choose y = 0:
x = 156 - 4(0) = 156
So, one possible pair of integers is x = 156 and y = 0.
Another possible pair of integers is x = 0 and y = 39.
There are multiple solutions to this problem as long as x + 4y equals 156.