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 5/2 times the amount he invested the first year. The third year, he invested $1,000 more than 1/5 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 than3/2 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 $1,400 more than 1/4of the amount Sam invested the first year. If Sam and Sally invested the same total amount at the end of three years, the amount Sam invested the first year is ___$ and the amount Sally invested the last year is ___$.

Answer 1

Year         Sam              Sally1:             X                    (3/2)X-10002:            (5/2)X-2000     2X-15003:             X/5+1000       X/4+1400Total         37X/10-1000    15X/4-1100
Since their investments are known to be equal, we equate the two totals and solve for X.37X/10-1000=15X/4-1100(150-148)X/40 = 1100-1000X/20=100X=2000
So Sam invested $2000 the first year.Sally invested X/4+1400=1900 in the last year.