A video merchant sold 24 cases of tapes, which was 20% of what he had left. What percent of tapes did he sell?

Mathematics

1 answer:

Naddika [18.5K]3 years ago

3 0

Answer:

16.67% of cases of tapes were sold.

Step-by-step explanation:

We are given the following in the question:

Number of cases of tapes sold = 24

Thus is 20% of tapes left.

Let x be the total number of tapes left.

Thus, we can write:

$20\%\rimes x = 24\\\\\dfrac{20}{100}\times x = 24\\\\x = 24\times 5 = 120$

Thus, total number of tapes =

$=24 + 120 = 144$

Percentage of tapes sold =

$=\dfrac{24}{144}\times 100\% = 16.67\%$

Thus, 16.67% of cases of tapes were sold.

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f(r) = (x -1)(x -4+√7)(x -4-√7)

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The signs of the terms are + - + -. There are 3 changes in sign, so Descartes' rule of signs tells you there are 3 or 1 positive real roots.

The rational roots, if any, will be factors of 9, the constant term. The sum of coefficients is 1 -9 +17 -9 = 0, so you know that r=1 is one solution to f(r) = 0. That means (r -1) is a factor of the function.

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f(r) = (r -1)(r -4 -√7)(r -4 +√7)

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<em>Comment on the graph</em>

I like to find the roots of higher-degree polynomials using a graphing calculator. The red curve is the cubic. Its only rational root is r=1. By dividing the function by the known factor, we have a quadratic. The graphing calculator shows its vertex, so we know immediately what the vertex form of the quadratic factor is. The linear factors are easily found from that, as we show above. (This is the "other means" we used to find the quadratic roots.)