Which of the following gives a valid reason for using the given solution method to solve the system of equations shown?

A test has 50 questions. each right answer is worth 2 points; each wrong answer deducts 0.5 points; blank answers are not counte

mestny [16]

ANSWER: There are 2 blank answers

EXPLANATION

Let

The number of right answers be ‘r’

The number of wrong answers be ‘w’

The number of blank answers be ‘b’

r + w + b = 50

This means r + w ≤ 50

Then we know,

Right answers = 2 marks

Wrong answers = -0.5 mark

Blank Answers = 0 marks

2r – 0.5w = 88.5

2r = 88.5 + 0.5w … (Equation I)

Since the score as .5, we know that there is at least one wrong answer, and the number of wrong answers is an odd number.

Since the score is 88.5, and each right answer gives 2 marks

There are at more than 44 (i.e. 88/2) right answers

Since r + w ≤ 50, and possible values of w are odd numbers

If r = 45, Possible values of w are 1, 3, and 5

If r = 46, Possible values of w are 1, 3

If r = 47, Possible values of w are 1, 3

If r = 48, The only possible value of w is 1

If r = 49,The only possible value of w is 1

Since 2r = 88.5 + 0.5w (Equation I)

We test for possible values:

If r = 45

2r = 88.5 + 0.5w

2(45) = 88.5 + 0.5w

90 = 88.5 + 0.5w

0.5w = 90 – 88.5

0.5w = 1.5

w = 3

So,

If there are 45 right answers

There are 3 wrong answers

r + w + b = 50

45 + 3 + b = 50

48 + b = 50

b = 50 – 48

b = 2

Then, there are 2 blank answers.

If r = 46

2r = 88.5 + 0.5w

2(46) = 88.5 + 0.5w

92 = 88.5 + 0.5w

0.5w = 92 – 88.5

0.5w = 3.5

w = 7

So,

If there are 46 right answers

There are 7 wrong answers

We know that r + w ≤ 50

46 + 7 = 53

So 46 and higher numbers are not possible solutions.

The only possible solution is:

There are 45 right answers

There are 3 wrong answers

<span>There are 2 blank answers</span>

6 0

2 years ago

On Saturday a library checked out 52 books.if 24 of the books were fiction what is the ratio of nonfiction books to fiction book

alukav5142 [94]

52-24=28 books were nonfiction
You must get the ratio if nonfiction to fiction
28/24= 7/6

5 0

3 years ago

A gallery has 25 paintings in its permanent collection, with display space for 10 at one time. How many different collections ca

Anastaziya [24]

You need to know in how many ways you can choose 10 out of 25 items when order does not matter. This is a combination problem.

$_{n}C_{r} = \dfrac{n!}{(n - r)!r!}$

$_{25}C_{10} = \dfrac{25!}{(25 - 10)!10!}$

$_{25}C_{10} = \dfrac{25 \times 24 \times 23 \times 22 \times 21 \times 20 \times 19 \times 18 \times 17 \times 16 \times 15!}{15! \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}$

$_{25}C_{10} = \dfrac{25 \times 24 \times 23 \times 22 \times 21 
\times 20 \times 19 \times 18 \times 17 \times 16}{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 
\times 2 \times 1}$

$_{25}C_{10} = \dfrac{23 \times 11 \times 20 \times 19 \times 2 \times 17}{1}$

$_{25}C_{10} = 23 \times 11 \times 20 \times 19 \times 2 \times 17$

$_{25}C_{10} = 3,268,760$

6 0

3 years ago

Read 2 more answers

A rectangle with length 11 feet and width 10 feet. A smaller rectangle with length 3 feet and width 2 feet is cut out of the lar

nikdorinn [45]

Answer:

b

Step-by-step explanation:

11 * 10 equals 110

3 * 2 equals 6

110 - 6 = 104

7 0