Question

Is Sam and sally invested the same amount at the end of three years , the amount same invested the first year is $ __ and amount sally invested the last year $ ___ .

Answer 1

First, let's find how much Sam saved per year:

First year: x

Second year: 5/2x - 2000

Third year: 1/5x + 1000

Second, let's find how much Sally saved per year:

First year: 3/2x - 1000

Second year: 2x - 1500

Third year: 1/4x + 1400

Since they save the same amount of money after the three years:

`x+(5)/(2)x-2000+(1)/(5)x+1000=(3)/(2)x-1000+2x-1500+(1)/(4)x+1400`

Now, let's put the terms with x in one side of the equation the terms without x in the other side.

`-2000+1000+1000+1500-1400=(3)/(2)x+2x+(1)/(4)x-x-(5)/(2)x-(1)/(5)x`

Solving the operations and using 20 as the common denominator:

`\begin{gathered} 100=(3)/(2)x+x+(1)/(4)x-(5)/(2)x-(1)/(5)x \\ (20*100=10*3x+20x+5x-10*5x-4x)/(20) \\ (2000=30x+20x+5x-50x-4x)/(20) \\ (2000=55x-54x)/(20) \\ (2000=x)/(20) \end{gathered}`

Since both sides have the same denominator, we can remove them:

`\begin{gathered} 2000=x \\ x=2000 \end{gathered}`

Sam saved $2000 in the first year.

Now, let's find out how much Sally invested in the third year.

Third year: 1/4x + 1400

Then,

`\begin{gathered} (1)/(4)*2000+1400 \\ 500+1400 \\ 1900 \end{gathered}`

Sally invested $1900 the last year.

Answer:

Sam saved $2000 in the first year.

Sally invested $1900 the last year.