Question

Kendra practiced her violin each day for a week. The first day she practiced 3/8 hours, the second day she practiced 1 1/4 hours, and the third day she practiced 2 1/8 hours. If she increased the time she practiced each day by the same amount, how much time did she practice the fifth day? Explain how you found your answer.

Answer 1

Hello there,

Alright so first we should write down what do we already know based on the problem:

- 1st day she practiced 3/8 hours

- 2nd day she practiced 1 1/4 hours

- 3rd day she practiced 2 1/8 hours

- she increased the time each day by the same amount

Now in order to solve the problem we first need to figure out by how much did she increase her practice time...

we would need to subtract day 2 practice from day 1

• 1 1/4 as an improper fraction is 5/4
• 5/4 written with a common denominator would be 10/8
• 10/8 - 3/8 = 7/8

So the common difference between the two days was 7/8 hours, that how much she increased from day 1 to day 2. Now in order to make sure that the difference among the tree is the same we would need to subtract day 3 by day 2...

• 2 1/8 as an improper fraction is 17/8
• 17/8 - 10/8 is 7/8

So yes the difference is 7/8 hours increased each day. Now we need find out how much she practiced on the FIFTH day.

• we add 7/8 with 7/8, since we last stopped at day 3
• we add 14/8 to 17/8 which would be 31/8 hours
• change 31/8 into a mixed number would be 3 7/8 hours

On the fifth day Kendra would practice for 3 7/8 hours.

Hope I helped,

Amna

Answer 2

Answer: she practiced for 3.875 hours on the fifth day.

Explanation:

If she increased the time she practiced each day by the same amount, it means that the time of practice is increasing in arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + d(n - 1)

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = 0.375

d = 1.25 - 0.375 = 0.875

n = 5(fifth day)

We want to determine the value of the 5th term, T5. Therefore,

T5 = 0.375 + 0.875(5 - 1)

T5 = 0.375 + 3.5

T5 = 3.875