One positive number is one-fifth of another number. The difference between the two numbers is 160, find the numbers.
x - x/5 = 160
4 x /5 = 160
x = 5 * 40 = 200
x/5 = 40
Why did the number go to therapy? Because it had issues and needed to find its positive side!
Let's call the two numbers x and y. According to the given information, we have the equation:
x = (1/5)y
We also know that the difference between the two numbers is 160, so we have:
x - y = 160
Now, we can substitute the value of x from the first equation into the second equation:
(1/5)y - y = 160
Multiplying both sides of the equation by 5 to get rid of the fraction:
y - 5y = 800
-4y = 800
Dividing both sides by -4:
y = -200
Now, substituting the value of y back into the first equation:
x = (1/5)(-200)
x = -40
So, the two numbers are -200 and -40.
Let's represent the first number as x and the second number as y.
According to the information given:
- One positive number is one-fifth of another number, which can be written as x = 1/5 * y.
The difference between the two numbers is 160, which can be written as:
- y - x = 160.
Now, let's solve the equations to find the values of x and y.
Substitute the first equation into the second equation:
- y - (1/5 * y) = 160.
Combine like terms:
- 5y - y/5 = 160.
Multiply both sides of the equation by 5 to remove the fraction:
- (5y - y/5) * 5 = 160 * 5.
- 25y - y = 800.
Simplify:
- 24y = 800.
Divide both sides of the equation by 24:
- y = 800 / 24.
- y = 33.33.
Substitute the value of y back into the first equation:
- x = 1/5 * 33.33.
- x = 6.67.
Therefore, the two numbers are approximately 6.67 and 33.33.
To find the numbers, let's assign variables to the unknown numbers. Let's call the smaller number "x" and the larger number "y".
According to the problem, one positive number is one-fifth of another number. In mathematical terms, this can be expressed as:
x = (1/5)y
The difference between the two numbers is 160. In math, the difference is found by subtracting one number from another. So we have:
y - x = 160
Now we have a system of two equations:
x = (1/5)y - Equation 1
y - x = 160 - Equation 2
To solve this system of equations, we can use substitution or elimination method.
Let's use the substitution method:
1. Substitute Equation 1 into Equation 2:
(1/5)y - x = 160
y - (1/5)y = 160
2. Simplify the equation:
(4/5)y = 160
3. Multiply both sides by (5/4) to isolate y:
y = (160) * (5/4)
y = 200
4. Substitute the value of y into Equation 1 to find the value of x:
x = (1/5) * 200
x = 40
Therefore, the smaller number (x) is 40, and the larger number (y) is 200.
So the numbers are 40 and 200.