The difference between two numbers is 44. Five times the smaller is equal to 8 more than the larger. What are the numbers
L = larger numbr
S = smaller number
The difference between two numbers is 44 mean:
L - S = 44
Five times the smaller is equal to 8 more than the larger mean:
5 S = L + 8
Now youust solve sytem of two equation with two unknow.
L - S = 44
5 S = L + 8
L - S = 44 Add S to both sides
L - S + S = 44 + S
L = 44 + S
5 S = L + 8
5 S = 44 + S + 8
5 S = 52 + S Subtract S to both sides
5 S - S = 52 + S - S
4 S = 52 Divide both sides by 4
S = 52 / 4 = 13
L = 44 + S = 44 + 13 = 57
let the smaller be x
let the larger be 44+x
translate:
"Five times the smaller is equal to 8 more than the larger"
----> 5x = 44+x + 8
4x = 52
x = 52/4 = 13
smaller is 13 , larger is 57
check
57-13 = 44 , check!!
5 times the smaller is 65
is 65 greater than 57 by 8 ?? , YES
Let's assume that the smaller number is x and the larger number is y.
The difference between the two numbers is 44, so we have the equation: y - x = 44.
We also know that five times the smaller number is equal to 8 more than the larger number, which can be expressed as: 5x = y + 8.
Now we can solve the system of equations.
First, let's solve the first equation for y in terms of x:
y = x + 44.
Substituting this expression for y into the second equation, we have:
5x = (x + 44) + 8.
Simplifying the equation:
5x = x + 52.
Subtracting x from both sides:
4x = 52.
Dividing both sides by 4:
x = 13.
Now we can substitute this value back into the first equation to find y:
y = x + 44 = 13 + 44 = 57.
Therefore, the two numbers are 13 and 57.
To solve this problem, let's assign variables to represent the unknown numbers. Let's call the larger number "x" and the smaller number "y".
According to the problem, the difference between two numbers is 44. This can be represented as:
x - y = 44 (Equation 1)
It is also stated that five times the smaller number is equal to 8 more than the larger number. This can be represented as:
5y = x + 8 (Equation 2)
Now, we have a system of equations:
Equation 1: x - y = 44
Equation 2: 5y = x + 8
We can solve this system of equations using substitution or elimination method.
Let's use substitution method to solve this system:
From Equation 1, we can rearrange it to express x in terms of y:
x = y + 44 (Equation 3)
Now, substitute Equation 3 into Equation 2:
5y = (y + 44) + 8
Simplify the equation:
5y = y + 52
Combine like terms:
5y - y = 52
4y = 52
Divide both sides by 4:
y = 52/4
y = 13
Now that we have the value of y, we can substitute it back into Equation 3 to find the value of x:
x = 13 + 44
x = 57
Therefore, the two numbers are 13 and 57.