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7nadin3 [17]
3 years ago
12

Rachel bought a soft drink for three dollars and six candy bars. She spent a total of $21. How much did each candy bar cost?

Mathematics
1 answer:
lubasha [3.4K]3 years ago
5 0
Let cost of each bar be m.
total amount spent = price of drink + price of bars
21 = 3 + 6m
21-3 = 6m
18 = 6m
m = 3$
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\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}

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We know that ,

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Volume =  \frac{1}{3}  \times  3.14  \times 9 \times 9 \times 13 \\  \\  \implies \: 1.05 \times 81 \times 13 \\  \\ \implies \: 1105.65 \: mm {}^{3}

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Or more accurately, it's a bit over 1.9 million.

===========================================================

Explanation:

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  • r = -5 = common ratio

Note that dividing any term by its previous term gets us the common ratio

  • r = term2/term1 = -25/5 = -5
  • r = term3/term2 = 125/(-5) = -5

The r value must stay the same the entire time, or else the sequence isn't geometric.

The nth term of any geometric sequence is a*(r)^(n-1). With the 'a' and 'r' values we found, we update that to 5(-5)^(n-1)

-----------------

To verify that is the correct nth term expression, plug in various values of n to compare it with the given sequence.

If we tried n = 2 for instance, then we find the 2nd term is

5(-5)^(n-1) = 5(-5)^(2-1) = -25

which matches what your teacher gave you. I'll let you verify the other terms.

-----------------

The last thing we need to do is plug in n = 9 and simplify

5(-5)^(n-1)

5(-5)^(9-1)

5(-5)^8

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