Juan's father is 4 times as old as Juan.Twenty-two years from now he will be twice as old as Juan.What are their ages now?
My work-
4(F)=J
22(2)=J
F = 4J
(F+22) = 2(J+22)
Substitute 4J for F in the second equation and solve for F. Insert that value into the first equation to solve for J. Check by putting both values into the second equation.
To solve this problem, we can set up a system of equations.
Let's represent Juan's current age as "J" and his father's current age as "F".
From the first statement, we know that Juan's father is 4 times as old as Juan. This can be written as: F = 4J
From the second statement, we know that twenty-two years from now, Juan's father will be twice as old as Juan. Mathematically, this can be written as: F + 22 = 2(J + 22)
Now we have a system of two equations:
1) F = 4J
2) F + 22 = 2(J + 22)
To solve this system, we can substitute the value of F from the first equation into the second equation. So instead of F, we can write 4J:
4J + 22 = 2(J + 22)
Next, let's distribute the 2:
4J + 22 = 2J + 44
Simplify by subtracting 2J from both sides:
2J + 22 = 44
Subtract 22 from both sides:
2J = 22
Divide both sides by 2:
J = 11
Now that we know Juan's age is 11, we can find his father's age using the first equation:
F = 4J
F = 4(11)
F = 44
Therefore, Juan's current age is 11 and his father's current age is 44.