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Svetach [21]
2 years ago
5

1. 5 Burgers and 3 orders of fries cost $34. 4 Burgers and 4 orders of fries cost $32. How much does each burger and each order

of fries cost?
2. A pile of 44 coins is made up of pennies, nickels, and dimes. If the pile is worth $3.07 and there are twice as many nickels as pennies, how many of each coin does the pile contain?
Mathematics
1 answer:
Elena L [17]2 years ago
7 0

Answer:

1.

a burger costs $5

an order of fries costs $3

2.

7 pennies

14 nickels

23 dimes

Step-by-step explanation:

x = price of a burger

y = price of a order of fries

5x + 3y = 34

4x + 4y = 32

=>

x + y = 8

x = 8-y

5×(8-y) + 3y = 34

40 - 5y + 3y = 34

-2y = -6

y = $3

x = 8 - 3 = $5

x = number of pennies

y = number of nickels

z = number of dimes

0.01×x + 0.05×y + 0.1×z = 3.07

y = 2x

x + y + z = 44

x + 2x + z = 44

3x + z = 44

z = 44 - 3x

0.01×x + 0.05×2x + 0.1×z = 3.07

0.11×x + 0.1×z = 3.07

0.11×x + 0.1×(44-3x) = 3.07

11x + 10×(44-3x) = 307

11x + 440 - 30x = 307

-19x = -133

x = 7

y = 2×7 = 14

z = 44 - 3×7 = 44 - 21 = 23

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                                    /  \
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                                       /  \
                                     2   28
                                          /  \
                                         2  14
                                              /  \
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So, the answer is 2 x 2 x 2 x 7 or 2^3 x 7
6 0
3 years ago
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>

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A rectangular prism of volume 3200 mm has a rectangular base of 10 mm and width 8 mm. Find the height h of the prism
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Answer:

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The rectangular prism of a rectangular box. The volume is given by the formula:

<u>Volume of Rectangular Prism</u> = length * width * height

Given Volume = 3200

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Width = 8

We need to find height. So we plug in the given information and find the height, in mm. Shown below:

Volume = Length * Width * Height

3200 = 10 * 8 * Height

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Height = 3200/80

Height = 40 mm

The height (h) = 40 mm

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7 0
2 years ago
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