Question 386382: julio is 4 times as old as maria his sister. in 6 years he will only be twice as old. how old is julio and maria now
Answer by gwendolyn(128)   (Show Source):
You can put this solution on YOUR website! We want to determine the ages of Julio and Maria, so we will assign them both variables:
let j= Julio's age
let m= Maria's age
Now, we can use these variables in equations. The problem states that Julio is four 4 times as old as Maria. This means that Julio's age is four multiplied by Maria's age. This can be set up as the equation below:
j=4m
We have two variables, so we need another equation. We also know that in six years, Julio's age will be twice (two times) Maria's age. The way to write this is a little bit more complicated. First, we have to remember that this equation is from "in 6 years." Because of this, we need to add 6 to each age. [(j+6); (m+6)] Since Julio's age six years from now will be twice Maria's age 6 years from now, we can write the equation as below:
j+6=(m+6)*2
Since we already know j's value in terms of m (from above, j = 4m), we can substitute 4m for the j in our second equation:
4m + 6 = (m + 6)*2
Both halves of the equation can be simplified.
First, we'll distribute the two in the second half of the equation:
4m + 6 = 2m + 2*6
Then we can multiply the 6 and 2 in the second half:
4m + 6 = 2m + 12
After that, we can subtract 6 from each side:
4m + 6 -6 = 2m + 12 - 6
4m = 2m + 6
Now, we can subtract 2m from both sides.
4m - 2m = 2m + 6 -2m
2m = 6
And divide each side by 2:
m =3
Therefore, Maria is 3 years old.
We also need to determine Julio's age. We know Julio is 4 times Maria's age so we can plug Maria's age into that equation:
j=4m
j = 4*3
j = 12
So, Julio is 12 years old and Maria is 3 years old.
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