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 ___$.
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.
When converting a variable to the other side of an equation, you change the sign completely. Since in the base equation it was -2x, it would be transitioned over and become 2x.
