the difference of two numbers is 37. the larger is one more than four times the smaller. what are the numbers?
smaller --- x
larger ---- 4x+1
solve 4x+1 - x = 37
To find the numbers, we can set up a system of equations based on the given information. Let's assume that the smaller number is represented by "x" and the larger number is represented by "y".
From the given information, we can derive the following equations:
Equation 1: "The difference of two numbers is 37." This can be written as: y - x = 37.
Equation 2: "The larger number is one more than four times the smaller." This can be written as: y = 4x + 1.
Now we have a system of two equations with two variables. We can solve this system to find the values of x and y.
To do that, we can solve Equation 1 for y:
y - x = 37
y = x + 37
Then we substitute this expression for y in Equation 2:
x + 37 = 4x + 1
Next, we can simplify the equation:
3x = 36
x = 12
Now that we have found the value of x, we can substitute it back into either equation to find the value of y:
y = 4x + 1
y = 4(12) + 1
y = 49
Therefore, the smaller number is 12 and the larger number is 49.