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3 years ago

Joseph wants to buy a new tennis

Mathematics

1 answer:

ludmilkaskok [199]3 years ago

8 0

Answer:

The shop made a profit about $40.

Step-by-step explanation:

Now, According to the question We know that :

The shop marked the $200 price up by 60%.

60% of $200 is = $120.

Now, the price is = $320 because, 200 + 120 = 320.

Joseph bought the tennis racket at 25% off.

25% of $320 is = $80.

Now, the discount price is = $240 Because, 320 - 80 = 240.

So, Joseph bought the racket for = $240.

Now we know that the original price from the factory was $200.

Joseph bought it for $240.

So, the shop made a profit of $40.

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Let

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and subtracting this from $S_n$ gives

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Now, we're given

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$a^2 + a^2r^2 + a^2r^4 + \cdots = 150 \implies 1 + r^2 + r^4 + \cdots = \dfrac{150}{a^2}$

We must have |r| < 1 since both sums converge, so

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Solving for r by substitution, we have

$\dfrac{15}a = \dfrac1{1-r} \implies a = 15(1-r)$

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$\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}$

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$\dfrac2{3(1-r)} = \dfrac1{1+r} \implies \dfrac{1-r}{1+r} = \dfrac23 \implies r = \dfrac15$

It follows that

$\dfrac a{1-r} = \dfrac a{1-\frac15} = 15 \implies a = 12$

and so the sum we want is

$ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}$

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?

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