Problem Solving

When a certain tree was first planted, it was 4 feet tall, and the height of hte tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree is 1/5 taller than it was at the end of the 4th year. By how many heet did the height of the tree increase each year?

3/10
2/5
1/2
2/3
6/5


Thanks in advance

P.S. How do I add an image without making it an attachment?

What we need to do is make an algebraic expression for: "At the end of the 6th year, the tree is 1/5 taller than it was at the end of the 4th year."

I am going to call the annual growth x.

The height of the tree after 4 years is: 4 ft + 4x
The height of the tree after 6 years is: 4 ft + 6x

We know that after 6 years, the tree is 1 1/5 times (or 6/5) the height of the 4th year.

So, we have (6/5)(4 + 4x) = 4 + 6x

Multiply both sides by 5, to get:

6(4 + 4x) = 20 + 30x

Multiply out to get:

24 + 24x = 20 + 30 x

Combine like terms to get:

4 = 6x

Divide by 6 to get 4/6 = x. So, 2/3 = x.

Let me know if you have questions,

Tatiana

thanks.

VP_Tatiana wrote:What we need to do is make an algebraic expression for: "At the end of the 6th year, the tree is 1/5 taller than it was at the end of the 4th year."

I am going to call the annual growth x.

The height of the tree after 4 years is: 4 ft + 4x
The height of the tree after 6 years is: 4 ft + 6x

We know that after 6 years, the tree is 1 1/5 times (or 6/5) the height of the 4th year.

So, we have (6/5)(4 + 4x) = 4 + 6x

Multiply both sides by 5, to get:

6(4 + 4x) = 20 + 30x

Multiply out to get:

24 + 24x = 20 + 30 x

Combine like terms to get:

4 = 6x

Divide by 6 to get 4/6 = x. So, 2/3 = x.

Let me know if you have questions,

Tatiana

Tatiana,

I got this question wrong as well. the main reason is I set the equation wrong. My equation is 4+6x-1/5(4+6x)=4+4x. The question says the tree was 1/5 taller than it was at the end of the 4th year. That is why I set the equation this way. Howwever, I don't get x=any answer choice, instead I got x=1.

so would you please explain how I initially set the quation wrong. I think 1/5 taller can mean minus right? I try to avoid making the mistake again on my gmat test. Help please.