The water level of Oshawa Creek is rising as the snow melts. On the first day of Spring, the creek rise a certain number of centimetres. One the second day, it rises 4 more centimetres than the amount it rose the first day. On the third day, it rose 4 more centimetres than it did on the second day, and so on. On the 5^("th ") day, the combined increase from the first 5 days of Spring was 5 centimetres higher than 1 metre (100cm). How many centimetres did the Oshawa Creek rise each day?

Question

The water level of Oshawa Creek is rising as the snow melts. On the first day of Spring, the creek rise a certain number of centimetres. One the second day, it rises 4 more centimetres than the amount it rose the first day. On the third day, it rose 4 more centimetres than it did on the second day, and so on. On the  5^("th ") day, the combined increase from the first 5 days of Spring was 5 centimetres higher than 1 metre  (100cm). How many centimetres did the Oshawa Creek rise each day?

Bytelearn · Accepted Answer

Denote Rise in Centimetres: Let's denote the number of centimetres the creek rose on the first day as x. According to the problem, on each subsequent day, the creek rises 4 more centimetres than the previous day. Therefore, we can express the rise in centimetres for the first five days as follows: Day 1: x cm Day 2: x + 4 cm Day 3: x + 4 + 4 = x + 8 cm Day 4: x + 8 + 4 = x + 12 cm Day 5: x + 12 + 4 = x + 16 cmCalculate Total Increase: The total increase in the water level over the first five days is the sum of the increases for each day. We can write this as an arithmetic series: Total increase = x + (x + 4) + (x + 8) + (x + 12) + (x + 16)Simplify Total Increase Expression: Simplify the expression for the total increase by combining like terms: Total increase = 5x + (4 + 8 + 12 + 16) Total increase = 5x + 40Set Up Equation: According to the problem, the total increase over the first five days is 5 centimetres more than 1 metre, which is 105 centimetres (since 1 metre = 100 centimetres). We can set up the equation: 5x + 40 = 105Solve for x: Now, we solve for x: 5x = 105 - 40 5x = 65 x = 65 / 5 x = 13Check Solution: We have found that x, the number of centimetres the creek rose on the first day, is 13 cm. To ensure we have answered the question prompt correctly, we can check the total increase over the first five days using the value of x: Total increase = 5x + 40 = 5(13) + 40 = 65 + 40 = 105 cm This matches the information given in the problem, so our solution is correct.

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