Laura is three times as old as Luci. In 5 years, the sum of their ages will be 30. What are the current ages of Laura and Luci? I need help!!
The answer to this is
Laura: 15 years
Luci: 5 years
Just blurting out an answer serves absolutely no purpose and goes against the
purpose of this webpage.
To me that is the same as claiming to be a real fan of a football team, never watching a game
simply looking at the score each week.
Luci's current age --- x
Laura's current age ---- 3x (it said : Laura is three times as old as Luci)
5 years from now:
Luci's age = x+5
Laura's age = 3x+5
it said: in 5 years from now, the sum of their ages will be 30 ----> x+5 + 3x+5 = 30
Now you have an equation to solve, which will give you the answer.
As a teacher, the above analysis is much more important to me than the answer.
To solve this problem, let's break down the information given step-by-step:
Step 1: Assign variables for Laura's and Luci's current ages.
Let's say Laura's current age is L, and Luci's current age is L/3 (since Laura is three times as old as Luci).
Step 2: Set up equations based on the given information.
In 5 years, Laura's age will be L + 5, and Luci's age will be L/3 + 5.
According to the problem, the sum of their ages in 5 years will be 30, so we can set up the equation: (L + 5) + (L/3 + 5) = 30.
Step 3: Solve the equation.
First, simplify the equation by combining like terms:
L + 5 + L/3 + 5 = 30.
Next, multiply each term in the equation by 3 to eliminate the fraction:
3(L + 5) + (L/3 + 5) = 30.
3L + 15 + L + 15 = 90.
Combine like terms:
4L + 30 = 90.
Subtract 30 from both sides of the equation:
4L = 60.
Divide both sides of the equation by 4:
L = 15.
Step 4: Calculate Laura's and Luci's current ages.
Since L is Laura's current age and we know that Luci is one-third of Laura's age, Luci's current age is L/3 = 15/3 = 5.
Therefore, Laura's current age is 15 years, and Luci's current age is 5 years.
To find the current ages of Laura and Luci, let's use algebraic equations.
Let's assume that Luci's current age is x. According to the information given, Laura is three times as old as Luci, so Laura's current age is 3x.
In five years, Luci's age will be x + 5, and Laura's age will be 3x + 5.
The sum of their ages in five years is 30, so we can write the equation:
(x + 5) + (3x + 5) = 30
Simplifying the equation:
4x + 10 = 30
Subtracting 10 from both sides of the equation:
4x = 20
Dividing both sides by 4:
x = 5
Therefore, Luci's current age is 5 years old.
To find Laura's current age, we substitute the value of x back into the equation:
Laura's age = 3x
Laura's age = 3 * 5
Laura's age = 15
Therefore, Laura is currently 15 years old, and Luci is currently 5 years old.