The difference between 2 numbers is 16. Five times the smaller is the same as 8 less than twice the larger. Find the numbers.
Just translate into math
larger --- x
smaller --- y
x-y = 16
5y = 2x - 8
from the first: y = x-16
5(x-16) = 2x - 8
5x - 80 = 2x - 8
3x = 72
x = 24 , then y = 8
the larger is 24, the smaller is 8
check:
difference is 24-8 = 16 , check!
five times the smaller = 40
twice the larger = 48
check!
Thank you
Let's assume the smaller number is x, and the larger number is y.
According to the given information, the difference between the two numbers is 16:
y - x = 16 ----(1)
It is also mentioned that five times the smaller number is the same as 8 less than twice the larger number:
5x = 2y - 8 ----(2)
Now we have a system of two equations. We can solve these equations using substitution or elimination method.
Let's solve the system using substitution method:
From equation (1), we have:
y = x + 16
Substituting this value of y in equation (2), we get:
5x = 2(x + 16) - 8
Simplifying the equation:
5x = 2x + 32 - 8
5x - 2x = 24
3x = 24
x = 8
Now substitute the value of x back into equation (1):
y - 8 = 16
y = 24
Therefore, the two numbers are 8 and 24.
To solve this problem, let's denote the smaller number as "x" and the larger number as "y". We can now translate the given information into equations.
1) "The difference between 2 numbers is 16":
This can be expressed as the equation: y - x = 16.
2) "Five times the smaller is the same as 8 less than twice the larger":
This can be expressed as the equation: 5x = 2y - 8.
Now, we have a system of two equations:
y - x = 16 (Equation 1)
5x = 2y - 8 (Equation 2)
To solve this system, we can use the method of substitution or elimination. Let's solve it using the substitution method.
From Equation 1, we can isolate y by adding x to both sides:
y = x + 16.
Now, substitute this expression for y in Equation 2:
5x = 2(x + 16) - 8.
Simplify the equation:
5x = 2x + 32 - 8,
5x - 2x = 24,
3x = 24.
Divide by 3 on both sides to solve for x:
x = 24 / 3,
x = 8.
Now that we have the value of x, substitute it back into Equation 1 to solve for y:
y - 8 = 16,
y = 16 + 8,
y = 24.
Therefore, the two numbers are 8 and 24.