The sum of two numbers is 56. The sum of the smaller and 5 times the larger is 192. Find the numbers.
5 b + s = 192
b + s = 56 so s = 56-b
5 b + 56 - b = 192
4 b = 136
b = 34
s = 22
To find the two numbers, let's call them x and y.
From the given information, we know that:
- The sum of the two numbers is 56, so we can write the equation: x + y = 56.
- The sum of the smaller number (x) and 5 times the larger number (5y) is 192, so we can write the equation: x + 5y = 192.
Now we have a system of two equations with two variables. To solve this system, we can use the method of substitution or elimination. Let's use substitution:
From the first equation, we can solve for x: x = 56 - y.
Substitute x in the second equation with 56 - y: (56 - y) + 5y = 192.
Now simplify the equation: 56 - y + 5y = 192.
Combine like terms: 56 + 4y = 192.
Subtract 56 from both sides: 4y = 136.
Next, divide both sides by 4: y = 34.
Now substitute the value of y back into the first equation to solve for x: x + 34 = 56.
Subtract 34 from both sides: x = 56 - 34.
Simplify: x = 22.
Therefore, the two numbers are 22 and 34.