The sum of two number is 110 .oneffifth of the larger number is 8 more than one ninth of the smaller number. Find the number
If the larger is x, then
x/5 = 8 + (110-x)/9
If one sixth of a number is 35 less than the third fourth of the number .find the number
Let's assume the larger number to be x and the smaller number to be y.
Given that the sum of the two numbers is 110, we have the equation:
x + y = 110 ...(Equation 1)
Also, it is given that one-fifth of the larger number is 8 more than one-ninth of the smaller number. Mathematically, this can be expressed as:
(1/5)x = (1/9)y + 8 ...(Equation 2)
To solve this system of equations, we can use the method of substitution.
Step 1: Solve Equation 1 for y in terms of x:
y = 110 - x
Step 2: Substitute the value of y in Equation 2:
(1/5)x = (1/9)(110 - x) + 8
Step 3: Simplify and solve for x:
9x = 5(110 - x) + 8 * 45
9x = 550 - 5x + 360
9x + 5x = 550 + 360
14x = 910
x = 910 / 14
x ≈ 65
Step 4: Substitute the value of x into Equation 1 to find y:
65 + y = 110
y = 110 - 65
y = 45
Therefore, the larger number is approximately 65 and the smaller number is 45.
To solve this problem, let's set up a system of equations.
Let's denote the larger number as "x" and the smaller number as "y."
According to the problem, the sum of the two numbers is 110: x + y = 110. (Equation 1)
It is also given that one-fifth of the larger number is 8 more than one-ninth of the smaller number: (1/5)x = (1/9)y + 8. (Equation 2)
To solve the system of equations, we can use the method of substitution.
Let's rearrange Equation 1 to express "x" in terms of "y": x = 110 - y.
Substituting this expression for "x" into Equation 2, we have:
(1/5)(110 - y) = (1/9)y + 8.
Now, we can solve this equation for "y."
Multiplying both sides of the equation by 45 (the least common multiple of 5 and 9) to eliminate the fractions, we get:
9(110 - y) = 5(y + 72).
Expanding both sides of the equation, we have:
990 - 9y = 5y + 360.
Combining like terms, we obtain:
990 = 14y + 360.
Subtracting 360 from both sides, we have:
630 = 14y.
Dividing both sides by 14, we get:
y = 45.
Now that we have found the value of "y" (the smaller number), we can substitute it back into Equation 1 to find the value of "x" (the larger number).
x + 45 = 110.
Subtracting 45 from both sides, we get:
x = 65.
Therefore, the larger number is 65, and the smaller number is 45.