The difference between two numbers is 25. The smaller number is 1/6th of the larger number. What is the value of the smaller number?
let x = larger number
let y = smaller number
then we set up the equations. since their difference is 25,
x - y = 25 : equation (1)
since the smaller is 1/6 of the larger,
y = (1/6)x : equation (2)
we substitute equation (2) to equation (1):
x - (1/6)x = 25
(5/6)x = 25
x = 25*6/5
x = 30
y = 5
hope this helps~ :)
Let's call the larger number L and the smaller number S.
Given that the difference between the two numbers is 25, we can write the equation:
L - S = 25
Also, it is given that the smaller number is 1/6th of the larger number, so we can write the equation:
S = (1/6)L
Now, we can solve the system of equations to find the value of the smaller number (S).
Substituting the second equation into the first equation, we have:
L - (1/6)L = 25
Multiplying through by 6 to eliminate the fraction, we get:
6L - L = 150
Simplifying the equation:
5L = 150
Dividing both sides of the equation by 5, we find:
L = 30
Substituting the value of L back into the second equation:
S = (1/6)(30) = 5
Therefore, the value of the smaller number (S) is 5.
To find the value of the smaller number, we can set up a system of equations based on the given information.
Let's assume that the larger number is represented by x, and the smaller number is represented by y.
From the first statement, "The difference between two numbers is 25," we can write the equation:
x - y = 25 (Equation 1)
From the second statement, "The smaller number is 1/6th of the larger number," we can write the equation:
y = (1/6)x (Equation 2)
Now we can solve this system of equations to find the value of the smaller number.
Substituting Equation 2 into Equation 1, we have:
x - (1/6)x = 25
Simplifying the left side of the equation:
(5/6)x = 25
To isolate x, we can multiply both sides of the equation by the reciprocal of (5/6), which is (6/5):
x = 25 * (6/5)
x = 30
Now that we have found the value of x, which represents the larger number, we can substitute this value back into Equation 2 to find the value of y, the smaller number:
y = (1/6) * 30
y = 5
Therefore, the value of the smaller number is 5.