The sum of their ages. is 97. The difference of their ages is 19. Find their ages.
B+L=97
B-L=19
the L cancel out, add the b together to get 2b
add 97 and 19 together
2b=116
divide both side by 2
b=58
plug 58 in any two equation for b
58+y=97
minus 58 from both sides
y=39
x+y=97
x-y=19
add them up:
2x = 116
x = 58
sub that into the first equation to find y
39
Well, isn't age just a number? And in this case, it seems like these numbers are having a bit of a math tango. Let's see if we can figure out their age game!
If the sum of their ages is 97 and the difference is 19, we can set up a good ol' math equation. Let's call the two mysterious ages x and y, assuming x is greater than y:
x + y = 97 (Equation 1)
x - y = 19 (Equation 2)
Now, let's do some magic to solve this conundrum. We can add Equation 1 and Equation 2 together:
2x = 116
Dividing both sides by two, we find:
x = 58
If x is 58, we can substitute it back into Equation 1:
58 + y = 97
Subtracting 58 from both sides, we have:
y = 39
Voila! The ages of these mystery people are 58 and 39. I hope this math circus brought a smile to your face!
To find the ages of the individuals, we can set up a system of equations using the information given.
Let's say the ages of the two individuals are represented by variables, such as "x" and "y".
1. The sum of their ages is 97:
x + y = 97
2. The difference of their ages is 19:
x - y = 19
To solve this system of equations, we can use the method of elimination or substitution.
Method 1: Elimination
By adding the two equations together, we can eliminate one variable:
(x + y) + (x - y) = 97 + 19
2x = 116
Dividing both sides by 2 gives us:
x = 58
Now, substitute the value of x back into one of the original equations:
58 + y = 97
Subtract 58 from both sides:
y = 39
So, the ages of the two individuals are 58 and 39.
Method 2: Substitution
You can solve the system of equations by substituting one variable in terms of the other:
From equation 2, we can express x in terms of y as:
x = y + 19
Now substitute this expression for x in equation 1:
(y + 19) + y = 97
Combine like terms:
2y + 19 = 97
Subtract 19 from both sides:
2y = 78
Divide both sides by 2:
y = 39
Now substitute the value of y back into the expression for x:
x = 39 + 19
x = 58
So, the ages of the two individuals are 58 and 39.