Question

Grandma swears she is getting younger. She has calculated that she is four times as old as I am now but remembers that 5 years ago she was five times as old as I was at that time. What is the sum of our ages now?

Answer 1

Explanation&Answer:

Getting younger which is negative (down/backward)

Four times as old as now

but... 5 yrs ago - Five times as old that yr ago

So... to make it easier we can use the number line

< -5 -4 -3 -2 -1 0 1 2 3 4 5 >

Add 4... we always start at ZERO

Which is positive 4

5 yrs ago which is at negative 1 ( -1 ).... Five times

So we will add 5... we will end at 4

ANSWER:

Positive FOUR (+4)

Answer 2

Let's use algebra to solve this problem.

Let x be my current age, and let y be Grandma's current age.

From the problem, we know that:

y = 4x (Grandma is four times as old as I am now)
y - 5 = 5(x - 5) (5 years ago, Grandma was five times as old as I was at that time)
We can use the first equation to substitute y in the second equation, which gives us:

4x - 5 = 5(x - 5)

Simplifying this equation, we get:

4x - 5 = 5x - 25

x = 20

Therefore, my current age is 20. Using the first equation, we can find Grandma's current age:

y = 4x = 4(20) = 80

The sum of our ages now is:

20 + 80 = 100

Therefore, the sum of our ages now is 100.