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3 years ago

How much money did she have at first

Mathematics

1 answer:

romanna [79]3 years ago

7 0

Step-by-step explanation:

x = the total money she had first.

x - x×1/4 - (x - x×1/4)×1/2 = 15

you see, first we needed to deduct 1/4 of x from x. that left us with (x - x×1/4). and from that we need to deduct 1/2.

now, we can simplify :

(x - x×1/4) = (x×4/4 - x×1/4) = x×3/4

x×3/4 - x×3/4 × 1/2 = 15

x×3/4 - x×3/8 = 15

we multiply both sides by 8 (4 is a factor of 8, so this handled both fractions perfectly) :

x×3×2 - x×3 = 120

6x - 3x = 120

3x = 120

x = $40

she had $40 at the beginning.

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Answer:

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Step-by-step explanation:

Let x be the side of square.

Length of box=8-2x

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Substitute the values then we get

Volume of box=V(x)= $(8-2x)(15-2x)x=(15x-2x^2)(8-2x)$

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Differentiate w.r.t x

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$12x^2-92x+120=0$

$3x^2-23x+30=0$

$3x^2-18x-5x+30=0$

$3x(x-6)-5(x-6)=0$

$(x-6)(3x-5)=0$

$x-6=0\implies x=6$

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Again differentiate w.r.t x

$V''(x)=24x-92$

Substitute x=6

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Substitute x=5/3

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Hence, the volume is maximum at x= $\frac{5}{3}$

Therefore, the side of the square , $x=\frac{5}{3}$ in cutout that gives the box the largest possible volume.

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Answer:

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