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:

$x+\frac{5}{2}x-2000+\frac{1}{5}x+1000=\frac{3}{2}x-1000+2x-1500+\frac{1}{4}x+1400$

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

$-2000+1000+1000+1500-1400=\frac{3}{2}x+2x+\frac{1}{4}x-x-\frac{5}{2}x-\frac{1}{5}x$

Solving the operations and using 20 as the common denominator:

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

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,

$\begin{gathered} \frac{1}{4}*2000+1400 \\ 500+1400 \\ 1900 \end{gathered}$

Sally invested $1900 the last year.

Answer:

Sam saved $2000 in the first year.

Sally invested $1900 the last year.