Alger is 7 years younger than abegail and the product of their age is 144.how old is each?
Abegail --- x years
Alger ---- x-7 years
x(x-7) = 144
x^2 - 7x - 144 = 0
(x - 16)(x + 9) = 0
x = 16 or x = -9, the last does not make sense.
sub back in my definitions
If Alger is x, then Abigail is x+7. So, just solve for x in
x(x+7) = 144
Note that 144 = 9*16
To find out the ages of Alger and Abegail, we can set up a system of equations based on the given information.
Let's assume that Alger's age is represented by variable A, and Abegail's age is represented by variable B.
According to the first statement, Alger is 7 years younger than Abegail. So we can write the equation as:
A = B - 7 (Equation 1)
According to the second statement, the product of their ages is 144. So we can write the equation as:
A * B = 144 (Equation 2)
Now, we can solve the system of equations by substitution or elimination method to find the values of A and B.
Using substitution method:
Substitute the value of A from equation 1 into equation 2:
(B - 7) * B = 144
Now, simplify the equation:
B^2 - 7B = 144
Rearrange the equation:
B^2 - 7B - 144 = 0
Now, we can factorize the equation:
(B - 16)(B + 9) = 0
Set each factor equal to zero:
B - 16 = 0 or B + 9 = 0
Solving these equations, we get:
B = 16 or B = -9
Since age cannot be negative, we disregard B = -9.
Therefore, Abegail's age (B) is 16.
Now, substitute this value back into equation 1 to find Alger's age (A):
A = B - 7
A = 16 - 7
A = 9
Therefore, Alger's age (A) is 9 and Abegail's age (B) is 16.