jack was 21 years older than kat. Together their ages totaled 161 years. What were their ages?
70 and 91
can you explain how you got it?
k + k + 21 = 161
2k = 161 - 21
2k = 140
k = 70
To solve this problem, we can use algebra. Let's assign variables to represent their ages. Let's say Jack's age is J years and Kat's age is K years.
According to the problem, Jack was 21 years older than Kat. This can be written as:
J = K + 21 (Equation 1)
The sum of their ages is 161:
J + K = 161 (Equation 2)
Now we have a system of two equations with two variables. We can solve this system using substitution or elimination.
Let's solve it using substitution:
Substitute Equation 1 into Equation 2:
(K + 21) + K = 161
Simplify the equation:
2K + 21 = 161
Subtract 21 from both sides:
2K = 140
Divide both sides by 2:
K = 70
Now, substitute this value of K back into Equation 1 to find J:
J = K + 21
J = 70 + 21
J = 91
So, Jack is 91 years old and Kat is 70 years old.