Question

Tim earned $300 in five days. After the first day, he earned $10 more each day than the day before. How much did Tim earn on the first day?

Answer 1

The given problem is based on arithmetic sequence
Sn = 300 (the sum of money in five days)
d = 10 (the difference day by day)
n = 5
The question asks how much Tim earn on the first day, we write it as a₁

The general formula to find the sum of a sequence is
n/2 (2a₁ + d(n-1)) = Sn

Input the numbers to the formula to find the value of a₁
n/2 (2a₁ + d(n-1)) = Sn
5/2 (2a₁ + 10(5-1)) = 300
5/2 (2a₁ + 10(4)) = 300
5/2 (2a₁ + 40) = 300
2a₁ + 40 = 300 × 2/5
2a₁ + 40 = 120
2a₁ = 120 - 40
2a₁ = 80
a₁ = 80/2
a₁ = 40

The first day, Tim earned $40

Answer 2

Use the equation 300⇒5x to find how much tim made each day on average.
x⇒60 so, Day 1: $60, Day 2: $70 etc.. so the equation 300=5x+10 suffices the problem. 300⇒5x+10 ⇒ 290=5x
x=58
So, Tim earned $58 his first day. Hope this helped.