the sum of two numbers is 58. the smaller number is 18 less then the larger number what are the numbers?
a = smaller number
b = larger number
a = b - 18
a + b = 58
b - 18 + b = 58
2 b - 18 = 58 Add 18 to both sides
2 b - 18 + 18 = 58 + 18
2 b = 76 Divide both sides by 2
2 b / 2 = 76 / 2
b = 38
a = b - 18
a = 38 - 18 = 20
smaller number = 20
larger number = 38
Why did the numbers go to therapy? Because they couldn't figure out how to communicate! Okay, let's solve this mystery.
Let's call the smaller number "x" and the larger number "y." According to the problem, we have two pieces of information:
1. The sum of the two numbers is 58: x + y = 58
2. The smaller number is 18 less than the larger number: x = y - 18
Now, armed with this information, let's substitute x from the second equation into the first equation:
(y - 18) + y = 58
2y - 18 = 58
2y = 76
y = 38
Great! Now that we know the larger number (y = 38), we can substitute it back into the second equation to find the smaller number (x):
x = y - 18
x = 38 - 18
x = 20
So the two numbers are 20 and 38! Now they can go back to their therapy session and talk about how proud they are for working together.
Let's solve this step-by-step:
Let's assume that the larger number is represented by 'x'.
According to the given information, the smaller number is 18 less than the larger number. So, the smaller number can be represented as 'x - 18'.
The sum of the two numbers is 58, so we can write an equation:
x + (x - 18) = 58
Now, let's simplify the equation and solve for x:
2x - 18 = 58
2x = 58 + 18
2x = 76
x = 76 / 2
x = 38
Therefore, the larger number is 38, and the smaller number can be found by subtracting 18 from the larger number:
38 - 18 = 20
So, the numbers are 38 and 20.
To solve this problem, let's assign variables to the two numbers. We can call the smaller number "x" and the larger number "y".
According to the problem, the sum of the two numbers is 58, so we can write an equation:
x + y = 58
We are also given that the smaller number (x) is 18 less than the larger number (y). Mathematically, we can express this as:
x = y - 18
Now we have two equations.
To solve this system of equations, we will use the method of substitution. We can substitute the value of x from the second equation into the first equation.
Substituting x = y - 18 into x + y = 58:
(y - 18) + y = 58
Now, simplify the equation:
2y - 18 = 58
2y = 58 + 18
2y = 76
Divide both sides of the equation by 2 to solve for y:
y = 76 / 2
y = 38
So the larger number (y) is 38.
To find the smaller number (x), we can substitute this value of y back into the second equation:
x = y - 18
x = 38 - 18
x = 20
Therefore, the smaller number (x) is 20, and the larger number (y) is 38.