Question

For three consecutive years, Sam invested some money at the start of the year. The first year, he invested x dollars. The second year, he invested $2,000 less than times the amount he invested the first year. The third year, he invested $1,000 more than of the amount he invested the first year.

During the same three years, Sally also invested some money at the start of every year. The first year, she invested $1,000 less than times the amount Sam invested the first year. The second year, she invested $1,500 less than 2 times the amount Sam invested the first year. The third year, she invested $1,400 more than of the amount Sam invested the first year.

If Sam and Sally invested the same total amount at the end of three years, the amount Sam invested the first year is $?
and the amount Sally invested the last year is $?
.

Answer 1

sam invested 4000 dollars the third year

Answer 2

To answer we let x be the amount of money that Sam invested during the first year.

Below are the expressions translated from the given word forms for the amount invested.

Sam:

2nd year : amount = 5x/2 - 2000

3rd year : amount = x/5 + 1000

The sum of money invested by Sam is:

x + (5x/2 - 2000) + (x/5 + 1000)

Similarly, we derive the expressions that we use for the amount that Sally invested.

Sally

1st year : amount = 3x/2 - 1000

2nd year : amount = 2x - 1500

3rd year : amount = x/4 + 1400

The total amount that Sally invested is,

total = (3x/2 - 1000) + (2x - 1500) + (x/4 + 1400)

Equating the two equations:

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

Solving for x,

x = 2000

For Sally's investment in the third year:

amount = x/4 + 1400 = (2000/4 + 1400) = 1900

ANSWERS:

Sam's first year = $2000

Sally's third year = $1900