An older person is seven years older than six times the age of a younger person. The sum of their ages is 21. Find ages
To solve this problem, let's assign variables to represent the ages of the older person and the younger person. Let's use "x" to represent the age of the younger person and "y" to represent the age of the older person.
According to the problem, the older person is seven years older than six times the age of the younger person. We can express this information with the equation:
y = 6x + 7
The sum of their ages is given as 21, so we can write another equation:
x + y = 21
Now, we have a system of two equations with two variables. We can solve this system using either substitution or elimination method. Let's use the substitution method:
Substitute the value of y from the first equation into the second equation:
x + (6x + 7) = 21
Combine like terms:
7x + 7 = 21
Now, isolate the variable:
7x = 21 - 7
7x = 14
Divide both sides by 7:
x = 2
Now that we have the value of x, we can substitute it back into one of the original equations to solve for y:
y = 6x + 7
y = 6(2) + 7
y = 12 + 7
y = 19
Therefore, the younger person is 2 years old, and the older person is 19 years old.
o + y = 21
o = 7 + 6 y
so
7 + 7y = 21
y = 2