fred is more than 3 years more than twice the age of jane. the sum of their ages is 48. how old is each?
f = 3+2j
f+j = 48
...
Substitute 3+2j for f in the second equation and solve for j. Insert that value into the first equation to solve for f. Check by putting both values into the second equation.
75
To solve this problem, we can break it down into two equations using the information given. Let's assign variables to represent their ages.
Let's say Fred's age is represented by 'F', and Jane's age is represented by 'J'.
According to the first piece of information, Fred is more than 3 years older than twice Jane's age:
F = 3 + 2J. (Fred is more than 3 years older than twice Jane's age)
The sum of their ages is given as 48:
F + J = 48. (The sum of their ages is 48)
Now we have a system of two equations:
Equation 1: F = 3 + 2J
Equation 2: F + J = 48
We can then solve this system of equations to find the values for F and J.
Substitute equation 1 into equation 2:
(3 + 2J) + J = 48
3 + 3J = 48
3J = 48 - 3
3J = 45
Divide both sides by 3:
J = 45 / 3
J = 15
Now substitute the value of J back into equation 1:
F = 3 + 2J
F = 3 + 2(15)
F = 3 + 30
F = 33
Therefore, Fred is 33 years old, and Jane is 15 years old.