The sum of 2 numbers is 31.⅔ of one of the numbers is equal to ⅝ of the other. Find the number
The answer is actually 15 and 16
To solve this problem, let's assign variables to the unknown numbers. Let's call one number "x" and the other number "y".
From the given information, we can write two equations:
Equation 1: x + y = 31 (The sum of the two numbers is 31)
Equation 2: (2/3)x = (5/8)y (2/3 of one number is equal to 5/8 of the other number)
To make things simpler, let's get rid of the fractions in Equation 2. We can do this by multiplying both sides by the least common multiple (LCM) of the denominators, which is 24:
(24)(2/3)x = (24)(5/8)y
(16x) = (15y)
Now, we have two equations:
Equation 1: x + y = 31
Equation 3: 16x = 15y
To solve this system of equations, we can use substitution or elimination. Let's use substitution:
Rearrange Equation 3 to solve for x:
x = (15/16)y
Substitute this expression for x in Equation 1:
(15/16)y + y = 31
Multiply through by 16 to get rid of the fraction:
15y + 16y = 496
31y = 496
Divide both sides by 31:
y = 16
Now substitute this value of y back into Equation 1 to solve for x:
x + 16 = 31
x = 31 - 16
x = 15
So, the two numbers are x = 15 and y = 16.