# Maths assignment on mixed problems questions 4,5,7a and 7b, 9,10,13,14 and showing all working out.

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4) 162.75 / 31 = $5.25 per student

5) a) 13.52 + 26.05 + x = 71.85

So, x = $32.28

b) 13.52 / 30 = Approx. $0.45 per day for gas

26.05 / 30 = $0.87 per day for electricity

7) a) Assuming fortnight means 2 weeks, assuming 52 1/7 weeks in a year:

52 1/7 * 1294.82 = 67,330.64

b) 322.85/1294.82 = Approx. 25% in taxes. So, Wendy would keep 75%. So, 67,330.64 * 75% = $50,497.98

9) 424 + 586 + 489 + 386 + x = 3000

So, x = 3000 - 424 - 586 - 489 - 36 = 1115 km

10) 23 hrs, 56 min, 4 sec would be 23:56:04

9 hrs, 50 min, 30 sec would be 9:50:30

Subtracting the two, we have to borrow a minute from the first one. So:

23:56:04 --> 23:55:64

So, 23:55:64 - 9:50:30 = 14:05:34, or 14 hours, 5 minutes, and 34 seconds. You have to be careful of the subtracting from 60 seconds and 60 minutes on problems like this. It doesn't occur here.

13) Various ways it can be done, all are similar. There is no math formula you can follow. Just plug in numbers until they work. One way is:

4, 9, 2

3, 5, 7

8, 1, 6

14) Since the sequence of numbers are similar, only adding 2 to each, then if we were to add 2 to each number in #13, we would get 21, what we are looking for. So:

6, 11, 4

5, 7, 9

10, 3, 8

4) Just divide the total money with the number of students: $162.75 / 31 = **$5.25**

5)a. The electricity and gas account was $71.85 subtract the cost of reading and electricity to get the cost of gas. So $71.85 - $13.53 - $26.05 = **$32.28**

b. To get the daily cost for both electricity and gas, subtract the cost of reading from the total and divide it by 30. $71.85 - $13.53 = $58.32 ; $58.32 / 30 = **$1.94**

7)a. There are 26 fortnights in one year, multiplied by her salary. So $1, 294.82 * 26 = **$33, 665.32 ** in one year.

b. Likewise, her tax of $322.85 in tax should be multiplied by 26 and deducted to her salary. So $322.85 * 26 = $8,394.10 ; $33, 665.32 - $8,394.10 = **$25, 271.22**

9. 424km + 586km +489km + 386km = 1,885km ; 3,000km - 1, 885 km = ** 1, 115km**

10. 23h 56 min 4s minus 9h 50 mins 30s = **13h 5min 34s**

13. 4, 9 ,2

3, 5, 7

8, 1, 6

14. 6, 11, 4

5, 7, 9

10, 3, 8

**4.** The problem says that there were 31 children who all paid equal amounts. If the total raised was $162.75, you would simply divide that by 31 students. The answer you get is **$5.25 per student**.

**5a**. For this, you have to take your total for the month, $71.85, and subtract the costs for reading the meter and the electricity. This will give you the cost for gas which is **$32.28**.

**5b.** For daily cost, you have to take the cost for just the electricity and for just gas, and divide each by 30 days. The electricity will cost about** 87 cents** per day (26.05/30) and the gas will be about **45 cents** per day (13.52/30).

**7a.** A fortnight refers to two weeks. So if Wendy makes $1,294.82 every two weeks and there are 52 weeks in a year, you would need to multiple her wage by half of 52 weeks, or 26. She will earn **$33,665.32** per year.

**7b.** For tax you would do the same thing as her wage. She gets tax every two weeks so you would multiply 26 weeks by her $322.85 in tax. She will receive **$8,394.1** in tax per year.

**9.** First you must add up how many km you have already traveled. So far you have traveled 1,885 km for those four days. If your total distance was 3,000 km you will have to travel **1,115 more km** (3,000-1,885).

**10.** For this problem I would start by converting everything to seconds. There are 60 seconds in a minute, so multiply each of the minute value by 60. There are 60 minutes in and hour so multiply all the hour values by 60, and then multiply by 60 again to get seconds. Add the values of each together to get the time in seconds it took for a full rotation.

Earth-(23*60*60)+(56*60)+(4)=86,164 seconds

Jupiter-(9*60*60)+(50*60)+(30)=35,430 seconds

Now to find the difference you have to subtract. Your difference will be 50,734 seconds. Now work backwards. Divide by 60 twice to get the number of hours (14 hours). Take the remainder (50,734-14 hours or 50,400 seconds) and divide by 60 to get the minutes (5 minutes). The remainder after that will be the seconds (334-5 minutes or 300 seconds) Your difference in time is **14 hours 5 minutes and 34 seconds.**

**13.** If the numbers are placed as follows, each row and column will add up to fifteen.

4, 9, 2

3, 5, 7

8, 1, 6

Just plug in the numbers and test it.

**14.** If the numbers are placed as follows, each row and column will add to be 21.

6, 11, 4

5, 7, 9

10, 3, 8