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 than 3/2 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 1/4 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 $ (fill in the blanks)

The amount Sam invested the first year is $2000 and the amount Sally invested the last year is $1900.

the balance is found at the link

step-by-step explanation:

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .