A sum of money is invested in a business. In each year, this investment earns 11 over 2 times as much as in the preceding year. If the investment earned a total of $29,250 in four years, how much did it earn in the fourth year?

Answer 1

earning in first year --- x
earining in 2nd year = 5.5x
earning in 3rd year = 5.5^2 x
earning in 4th year = 5.5^3 x

x(1 + 5.5 + 5.5^2 + 5.5^3) = 29250
inside the bracket is a GP, but since there are only 4 times, we might as well just add them up

x(203.125) = 29250
x = 144
so in the 4th year they earned 5.5^3(144) or 23,958

check:
in first year --- 144
in 2nd year --- 792
in 3rd year --- 4356
in 4th year --- 23958
add them up to get 29,250

Answer 2

1. A sum of money is invested in a business. In each year this investment earns 1 times as much as in the preceding year. If the investment earned a total of $29,250 in four years, how much did it earn in the fourth year?
• CORRECT: $12,150
How to get it is to find out the original investment and do that by the following steps
amount= origamount*1.5^timeInYears

so in four years, amount=orig*1.5^4
earned=amount-orig=orig^1.5^4-orig
29250=orig (1.5^4-1)
29250=x(1.5^4-1)
Let's solve your equation step-by-step.
29250=x(1.54−1)
Step 1: Simplify both sides of the equation.
29250=4.0625x
Step 2: Flip the equation.
4.0625x=29250
Step 3: Divide both sides by 4.0625.
4.0625x
4.0625
=
29250
4.0625
x=7200

Witch is 7200 then times it by 1.5^4 then
7200(1.54−1.53)
=(7200)(1.54+−3.375)
=(7200)(1.54)+(7200)(−3.375)
=36450−24300
=12150