SOLUTION:
Lara’s mother is 26 years older than her. Six years ago she was three times as old as Lara. Determine both Lara and her mother’s age now, using an algebraic equation. Show
Question 1169685:
Lara’s mother is 26 years older than her. Six years ago she was three times as old as Lara. Determine both Lara and her mother’s age now, using an algebraic equation. Show ALL steps!
lara's mother is 26 years older than lara.
x = y + 36
6 years ago, age of lara'a mother was 3 times age of lara.
x - 6 = 3 * (y - 6)
replace x in this equation with the equivalent value of y + 36 to get:
y + 26 - 6 = 3 * (y - 6)
simplify to get:
y + 20 = 3y - 18
add 18 to both sides of the equation and switch sides to get:
3y = y + 38
subtract y from both sides of the equation to get:
2y = 38
solve for y to get:
y = 19
since x = y + 26, then:
x = 45
you have:
x = 45
y = 19
that should be your answer.
confirm below.
age of lara's mother is 45 which is 26 years older than age of lara.
since lara is 19, then 19 + 26 = 45.
this confirms that lara's mother is 26 years older than lara.
6 years ago, lara was 13 and lara's mother was 39.
39 is 3 * 13.
this confirms that lara's mother was 3 times as old as lara 6 years ago.
solution is confirmed to be good.
solution is:
lara is 19
lara's mother is 45.
Lara’s mother is 26 years older than her. Six years ago she was three times as old as Lara. Determine both Lara and her mother’s age now, using an algebraic equation. Show ALL steps!
Let Lara's age be L
Then her mother's is: L + 26
We then get: L + 26 - 6 = 3(L - 6)
L + 20 = 3L - 18
L - 3L = - 18 - 20
- 2L = - 38
Lara, or
You should now be able to find the mother's age!
Here is way to set up and solve this problem using algebra that is completely different from the methods shown by the other tutors.
The problem says that Lara's mother was three times as old as Lara 6 years ago. So start the problem with
x = Lara's age 6 years ago
3x = her mother's age 6 years ago
Then use the fact that the difference in their ages is (and always will be) 26 years:
ANSWER: 6 years ago, Lara was 13, so now she is 19. Her mother is 26 years older, so she is 45.
The required algebra in this solution is much simpler than what is required in the other solutions you have been shown.
That's a good example of how you should always be looking for alternative ways to solve problems -- you might find a method that works better than the way you have always used before.
And that lesson doesn't hold only for solving math problems. It is applicable to solving any problems life might throw at you....