the second part to my homework?

Question

(3)Jason had to submit five animation projects as per his syllabus in the final semesters. He scored 82, 85, 78, and 88 points out of 100 in four projects. What should be his score in the fifth project so that the average of all the projects is at least 85?

(4)Martha wants to buy a digital camera from her three-month savings. To do this she needs to maintain an average saving of $300 in each month. She saves $450 in the first month and $200 in the second month. Find the amount she should save in the third month to buy a digital camera at the end of three months.

Answer 1

Remember that the formula for average of 5 numbers goes as follows:

If V is average, and the 5 scores are a, b, c, d, and e, the formula is

V = (a + b + c + d + e)/5

That is, the sum of the scores, all divided by 5.

With that in mind, we're given 4 of the 5 tests, and we're given our desired average. That means
V = 85, a = 82, b = 85, c = 78, d = 88. Therefore,

85 = (82 + 85 + 78 + 88 + e)/5

All you have to do is solve for e. Let's add the numbers in brackets together.

85 = (333 + e)/5

Multiply both sides by 5,

425 = 333 + e

Solve for e.

e = 425 - 333
e = 92

The required score is 92.

Answer 2

(3) Jason had to submit five animation projects as per his syllabus in the final semesters. He scored 82, 85, 78, and 88 points out of 100 in four projects. What should be his score in the fifth project so that the average of all the projects is at least 85?

Let x = to be scored in the 5th project.
(82 + 85 + 78 + 88 + x) / 5 => 85
333 + x => 425
x => 92

Answer: He should score at least 92.

Proof:
= (82 + 85 + 78 + 88 + 92) / 5
= 425 / 5
= 85

(4)Martha wants to buy a digital camera from her three-month savings. To do this she needs to maintain an average saving of $300 in each month. She saves $450 in the first month and $200 in the second month. Find the amount she should save in the third month to buy a digital camera at the end of three months.

= ($300 * 3) - ($450 + $200)
= $900 - $650
= $250

Answer: She should save $250 in the 3rd month.

Proof:
$300 * 3 = $450 + $200 + $250
$900 = $900

Answer 3

Total of 4 subjects = 82+85+78+88 = 333
Let marks in 5th sub = x
Total of 5 subjects = 333 + x
Avg. of 5 subjects = 5 × 85 =425
333 + x = 425
x = 92

Total saving = Avg. × Months = 3 × 300 = 900
Total of 2 months = 450 + 200 = 650
She should save 900 – 650 = 250 in the 3rd month.

Answer 4

3. We know that 82+85+78+88 +a/5=85

Work the problem by adding what we have so far:

(333+a)/5=85

multiply by 5

333+a=425

-333

a=92

You would have to get at least 92 on the last project.


4. 300= 450+200 +a/ 3

300=(650+a)/3

multiply by 3

900= 650 + a

250=a

She will need to save $250 to get that camera.

Answer 5

For both of these, remember that average = total divided by number of units in question;

a) 85 (desired average) X 5 (total number of tests) = 425

425 - (82 + 85 + 78 + 88) = 92

b) $300 (desired average) X 3 (total number of months) = $900

$900 - ($450 + $200) = $250

Answer 6

(3)
(82 + 85 + 78 + 88 + x) / 5 = 85 [Calculated Average]

Notice that the divisor is equal to the number of terms in the numerator. Solve for x. [Do this question yourself for practice]

(4)

(450 + 200 + x) / 3 = 300
650 + x = 900
x = 250

Answer 7

3) Jason needs at least a 92 on the last project.

4) Martha needs to save at least 250 in the last month.