SOLUTION: A family bought 4 sodas at a movie theatre for a total of $9.30. they bought one small, one medium and one large and one jumbo size. the jumbo cause twice as much as the medium, t

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Question 1113592: A family bought 4 sodas at a movie theatre for a total of $9.30. they bought one small, one medium and one large and one jumbo size. the jumbo cause twice as much as the medium, the medium costs 70 cents more than the small and the large costs twice as much as the small. what are the price of each soda?
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
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prices:
w, x, y, z
small medium large jumbo

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4 sodas at a movie theatre for a total of $9.30. they bought one small, one medium and one large and one jumbo size.
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w%2Bx%2By%2Bz=9.3


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the jumbo COSTS twice as much as the medium, the medium costs 70 cents more than the small and the large costs twice as much as the small.
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system%28z=2x%2Cx=w%2B0.7%2Cy=2w%29


Find price of each.
system could start as
system%28w%2Bx%2By%2Bz=9.3%2Cz=2x%2Cx=w%2B0.7%2Cy=2w%29
.

substituting for y and z,
w%2Bx%2B2w%2B2x=9.3
3w%2B3x=9.3
w%2Bx=3.1----------equation in two variables, w and x.


Revise to the simpler system,
system%28w%2Bx=3.1%2Cx=w%2B0.7%29

Use simple substituion:
w%2Bw%2B0.7=3.1
2w=3.1-0.7
highlight%28w=1.2%29

Use this value for w to find all the other price values.

Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let x = small soda cost/price), in dollars.

Then the medium soda costs (x+0.7);

     the large  soda costs 2x;

     the jumbo size  costs 2*(x+0.7).


x + (x+0.7) + 2x + 2*(x+0.7) = 9.30

x + x + 0.7 + 2x + 2x + 1.4  = 9.30

6x + 2.1 = 9.30

6x = 9.30 - 2.1 = 7.2  ====>  x = 7.2%2F6 = 1.2.


Thus small soda costs 1.2 dollars.  


Based on it, calculate the cost of other sodas on your own.


The lesson to learn from the solution is THIS: 

    This problem is for one unknown. It is not for 4 unknowns and not for using systems of equations.



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
one small, one medium and one large and one jumbo size. the jumbo cause twice as much as the medium, the medium costs 70 cents more than the small and the large costs twice as much as the small. what are the price of each soda?
With M being the price of the medium, jumbo = 2M, small = M - .7, and large = 2(M - .7), or 2M - 1.4

We then get: M + 2M + M - .7 + 2M - 1.4 = 9.3

6M - 2.1 = 9.3

6M = 11.4



Cost of each jumbo: highlight_green%28matrix%281%2C3%2C+2%281.9%29%2C+%22=%22%2C+%22%243.80%22%29%29

Cost of each small: highlight_green%28matrix%281%2C3%2C+1.90+-+.70%2C+%22=%22%2C+%22%241.20%22%29%29

Cost of each large: highlight_green%28matrix%281%2C3%2C+3.80+-+1.40%2C+%22=%22%2C+%22%242.40%22%29%29

There it is!!! No COMPLEXITIES!