Question

Allison practices her violin for at least 12 hours per week. She [practices for three fourths of an hour each session. If Allison has already practiced 3 hours this week, how many more sessions remain for her to meet or exceed her goal?

Please show the Inequality

Answer 1

Well let’s see...

If she practices 3/4 of an hour a week we need to find out how much time is 3/4 of an hour. To do this we divide 60/4 and get 15. We check by multiplying 15 x 4 and get 60 so we know we are correct.

Now we know that 1/4 of an hour is 15 minutes, but we need to know how long she practices per session. Because 15 is 1/4 we multiply 15 x 3 to make it 3/4.

15 x 3 is 45. We check by dividing 45 by 3 and we do get 15 so we are correct.

If 3/4 of an hour is 45 minutes and she practices for 3/4 of an hour then we know that for every session she practices for 45 minutes.

The question states that she practices for 3 hours every week, since we know that we need to multiply 45 (because she practices 45 minutes every session) by a number that will get us 3 hours.

45 x 4 is 180 minutes (or three hours) we divided 180 by 4 and got 45 thus we are correct.

Which in turn means she has done 4 sessions this week. Since now we know that 4 sessions is 3 hours (making the ratio 4:3) we can multiply to find how many sessions she has left to do this week.

So if we have 4:3 then we can make it 8:6 (which means we know have 8 sessions and 6 hours) now we can make it 12:9 (12 sessions and 9 hours) and add it once more to get 16:12 (or 16 sessions and 12 hours).

Now we know that it takes 16 sessions for her to reach twelve hours, and since she and already done 4 sessions and 3 hours, it means that she has 12 sessions left to do until she is able to get her 12 hour a week goal.

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Hope this helped, have a great day! :D

Answer 2

`3+(3)/(4)x\geq 12`

Explanation:

Given,

The number of hour he already practiced in this week = 3,

Also, she practices for three fourth of an hour each session,

If x be the number of remaining session,

So, the additional number of hours he practiced in this week =
`(3x)/(4)`

Thus, the total number of hours he practiced in this week =
`3+(3x)/(4)`

According to the question,

Total number of hours ≥ 12 hours

`\implies 3+(3x)/(4)\geq 12`

Which is the required inequality.