Write a system of equations to model the problem and solve the system:
The sum of two numbers is 156. What number is 28 more than the second number. What are the numbers?
x+y = 156
x = y+28
To model this problem with a system of equations, we can first define two variables to represent the two numbers. Let's call the first number x, and the second number y.
From the given information, we can form two equations:
1) The sum of two numbers is 156:
x + y = 156
2) The first number is 28 more than the second number:
x = y + 28
Now, we can solve this system of equations to find the values of x and y.
We have two options to solve this system: substitution or elimination method. Let's use the substitution method.
Using the second equation, we can rewrite it as y = x - 28. Now, substitute this value of y into the first equation:
x + (x - 28) = 156
2x - 28 = 156
2x = 156 + 28
2x = 184
x = 184 / 2
x = 92
Now that we have the value of x, we can substitute it back into the second equation to find the value of y:
y = x - 28
y = 92 - 28
y = 64
Hence, the two numbers are 92 and 64.