M is 5 years older than N. The product of their ages is 84. How old is M?
N + 5 = m
m + n = 84
(n + 5) + n = 84
2n+5= 84
solve for n and then subtract from 84 to find m.
Holdup I didn't read that right
n + 5 = m
nm = 84
n=84/m
84/n= n +5
84= n^2 + 5n
n^2 + 5n - 84 = 0
Use quadratic equation or complete the square and you get n = 7 so M = 12
7x12=84
To find the age of M, we need to solve the given puzzle.
Let's start by setting up equations based on the information given:
1. M is 5 years older than N: M = N + 5
2. The product of their ages is 84: M * N = 84
Now we can solve these equations simultaneously to find the values of M and N.
To find the age of M, let's substitute equation 1 into equation 2:
(N + 5) * N = 84
Expanding the equation:
N^2 + 5N = 84
Rearranging the equation:
N^2 + 5N - 84 = 0
Now, we need to find two numbers whose product is -84 and their sum is 5. By factoring or using the quadratic formula, we can determine the values of N:
(N + 12)(N - 7) = 0
So either N + 12 = 0 or N - 7 = 0.
If N + 12 = 0, then N = -12 (which is not a valid age).
If N - 7 = 0, then N = 7.
Now, we know that N = 7. We can substitute this value back into equation 1 to find M:
M = N + 5
M = 7 + 5
M = 12
Therefore, M is 12 years old.