Question

Any smart people out there, i really suck at these problems... Five times Lauren's age, decreased by 2 is equal to two times Lauren's age, increased by 11. How old is Lauren?

Answer 1

Take it slowly, one step at a time.

First, you need to pick something to call "Lauren's age",
because you don't know what number it is. I have a bright idea !
Let's call Lauren's age ' L ' ! OK ?

Use ' L ' to build the quantities discussed in the question:

Five times Lauren's age . . . . . . . . . . . . . . . . . 5 L
Five times Lauren's age, decreased by 2 . . . 5L - 2

Two times Lauren's age . . . . . . . . . . . . . . . . . 2 L
Two times Lauren's age, increased by 11 . . . 2L + 11

The question says that these 2 quantities are equal,
so write that down:
5L - 2 = 2L + 11

Add 2 to each side: 5L = 2L + 13

Subtract 2L from each side: 3L = 13

Divide each side by 3 : L = 13/3 or 4 and 1/3 .

That's certainly a weird number, but you can
check it out, and you'll find that it's true:

Lauren's age . . . . . 13/3

Five times Lauren's age . . . . . . . . . . . . . . . . . 65/3
Five times Lauren's age, decreased by 2 . . . 59/3 <===

Two times Lauren's age . . . . . . . . . . . . . . . . . 26/3
Two times Lauren's age, increased by 11 . . . 59/3 <===

Those 2 quantities are equal. So Lauren is 4-1/3 years old, by golly !

Answer 2

Set Lauren's age equal to L.


Using what the problem gave us, we can quickly set up an equation:

5L - 2 = 2L

Solving this equation, we get 3L = 2. L = 2/3 Lauren is 2/3 of a year old.