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Sidana [21]
3 years ago
13

Justine and Roy both ordered takeout dinners for their family. Justine paid $15 for three sodas and three burgers. Roy paid $12

for four sodas and two burgers. Equations representing this situation are given below, where x represents the cost of a soda and y represents the cost of a burger. Find out how much it costs to purchase 1 hamburger and 1 soda.
3x+3y=15
4x+2y=12
Mathematics
1 answer:
Andrej [43]3 years ago
3 0

Answer:

The cost of 1 soda is  : x = $ 1

The cost of 1 hamburger is : y = $4

Step-by-step explanation:

Here, the given set of equations is:

3 x + 3 y = 15   ........  (1)

4 x + 2 y = 12    ......  (2)

Here, x represents the cost of a soda.

  and y represents the cost of a burger.

Now, solving the given system of equation by ELIMINATION METHOD.

Multiply (1) with 4 and (2) with -3 , we get:

12 x + 12 y = 60   ........  (a)

-12 x  - 6 y = - 36    ......  (b)

Adding both equations,we get:

12 x + 12 y  -12 x  - 6 y = - 36 +  60

or, 6 y = 24

or, y = 34/6  = 4

or, y = 4

Putting the value of y =  4 in (1) , w e get:

3 x + 3 y = 15  ⇒  3 x +  3 (4) = 15

or, 3 x = 15 - 12 = 3

or, x  = 3/ 3  = 1, or x  =  1

Hence, here, the cost of 1 soda is  : x = $ 1

And the cost of 1 hamburger is : y = $4

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THE SMALLEST FORMS:

- smallest prism ---> the cube with all sides 2 ==> the volume is 2*2*2 = 8 cm^3

- smallest pyramid number one ---> the pyramid with base sides 2 and the height also 2 ==> the volume is (1/3)*2*2*2 = 8/3 cm^3

- smallest pyramid number two ---> the pyramid with base sides 2 and the lateral sides also 2 ==> the radius of the base is sqrt(2) ==> [pyramid_height]^2 = [lateral_side]^2 - [base_radius]^2 = 2^2 - sqrt(2)^2 = 4 - 2 = 2 ==> pyramid_height = sqrt(2) ==> the volume is (1/3)*2*2*sqrt(2) = 4*sqrt(2)/3 cm^3

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The lesser volume is the volume of the smallest pyramid number two. ==> it's wax cost is approximately 0.0075 * 4 * 1.42 / 3 $ per candle = 0.014 $ per candle ==> the total cost  per candle is approximately 0.014 + 1.6 = 1.614 $ per candle.

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- biggest pyramid number two ---> the pyramid with base sides 10 and the lateral sides also 10 ==> the radius of the base is 5*sqrt(2) ==> [pyramid_height]^2 = [lateral_side]^2 - [base_radius]^2 = 10^2 - [5*sqrt(2)]^2 = 100 - 50 = 50 ==> pyramid_height = 5*sqrt(2) ==> the volume is (1/3)*10*10*5*sqrt(2) = 500*sqrt(2)/3 cm^3

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The range of the cost is the interval [1.614 ; 9.1]. Depending on other prices on the market,  you greed, and other factors you will put a profit margin: maybe 20% of the cost ; maybe a fixed margin like 5$. So the price per candle will be the cost per candle plus the profit margin per candle.

If I were to choose the base length I would have to say 6 because it is the arithmetic mean between 2 and 10: (2+10)/2 = 12/2 = 6. 2cm is too small, and 10cm is too big.

Also if you start with a rectangle of length 10 and width 2 and you have to find the rectangle with the largest area by being allowed to increase the width and decrease the width with the same quantity you get this:

Area of the new rectangle is (10-x)(2+x) = -x^2 + 8x + 20 = -x^2 + 8x -16 + 36 = -(x^2 - 2*x*4 + 4^2) + 36 = -(x-4)^2 + 36 = 36 - (x-4)^2 which has the maximum value of 36 because out of 36 you subtract a positive value. You get the maximum when (x-4)^2 = 0 ==> x-4=0 ==> x=4

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