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Iteru [2.4K]
2 years ago
11

I need help with this...

Mathematics
1 answer:
solniwko [45]2 years ago
4 0
This can be represented as the equation
x/48 + 1/3 = 47/48

In order to solve this we need to siolate x ( get x in one side of the equation by itself and the rest in the other)

We can do that by subtracting 1/3 from both sides of the equation, by doing this we eliminate 1/3 from the left side of the equation and since we did it on both sides of the equations, it still is an equation ( one side equals the other )

x/48 + 1/3 - 1/3 = 47/48 - 1/3
1/3 - 1/3 cancel out, so we get
x/48 = 47/48 - 1/3
To subtract 47/48 - 1/3 ( and all other equations), the denominator of all fractions need to be the same. We can make the denominators equal by setting 1/3 as 16/48, which is the same thing as 1/3.

x/48 = 47/48 - 16/48
x/48 = 31/48

Now to fully isolate x, we can just multiply both sides by 48, so the x/48 turns into 48/48x or just x, and the 31/48 just turns into 31.
x = 31 x 48/48
x = 31

so 31/48 + 1/3 = 47/48
This was quite long but I hope it helps if you didnt understand how to solve equations
:)
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we have that

300 + 150 + 75 +...

Let

a1=300\\ a2=150\\ a3=75

we know that

\frac{a2}{a1} =\frac{150}{300} \\\\ \frac{a2}{a1}=0.5 \\ \\ a2=a1*0.50

\frac{a3}{a2} =\frac{75}{150} \\\\ \frac{a3}{a2}=0.5 \\ \\ a3=a2*0.50

so

a(n+1)=an*0.50

Is a geometric sequence

Find the value of a4

a(4)=a3*0.50

a(4)=75*0.50

a(4)=37.5

Find the value of a5

a(5)=a4*0.50

a(5)=37.5*0.50

a(5)=18.75

Find S5

S5=a1+a2+a3+a4+a5\\ S5=300+150+75+37.5+18.75\\ S5=581.25

therefore

the answer is

581.25

Alternative Method

Applying the formula

S_n=\frac{a_1 (1-r^n)}{1-r} \\\\a_1=300 \\ r=\frac{1}{2}\\\\ S_5=\frac{300(1-(\frac{1}{2})^5)}{1-\frac{1}{2}}\\\\=\frac{300(1-\frac{1}{32})}{\frac{1}{2}}\\\\=\frac{300 \times \frac{31}{32}}{\frac{1}{2}}\\\\=\frac{75 \times \frac{31}{8}}{\frac{1}{2}}\\\\=\frac{\frac{2325}{8}}{\frac{1}{2}}\\\\=\frac{2325}{8} \times 2\\\\=\frac{2325}{4}\\\\=581 \frac{1}{4}\\\\=581.25

therefore

the answer is

581.25

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