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Sholpan [36]
3 years ago
11

How do you solve 4x+10=3x+37

Mathematics
1 answer:
lisov135 [29]3 years ago
7 0

Answer:

x = 27

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Order of Operations: BPEMDAS

<u>Algebra I</u>

  • Equality Properties

Step-by-step explanation:

<u>Step 1: Define equation</u>

4x + 10 = 3x + 37

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Subtract 3x on both sides:                    x + 10 = 37
  2. Subtract 10 on both sides:                     x = 27

<u>Step 3: Check</u>

<em>Plug in x to verify it's a solution.</em>

  1. Substitute:                    4(27) + 10 = 3(27) + 37
  2. Multiply:                        108 + 10 = 81 + 37
  3. Add:                               118 = 118

And we have our final answer!

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The interest rate is 6.992%, if a bank advertises that it compounds money quarterly and that it will take Double your money in 10 years.

Step-by-step explanation:

The given is,

                          Compounds money quarterly

                          Double your money in 10 years

Step:1

              Formula to calculate future investment with compounded quarterly,

                                                        A =P(1+\frac{r}{n} )^{nt}...............................(1)

              Where, A - Future amount

                           P - Initial investment\

                            r - Rate of interest

                            n - No. of compounding in a year

                             t - No. of years

Step:2

               Let, P = X

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              From given, n - 4 ( for compounding quarterly )

                                    t - 10 years

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                                                        2X =X(1+\frac{r}{4} )^{(4)(10)}

                                                         \frac{2X}{X}  =(1+\frac{r}{4} )^{(4)(10)}

                                                            2  =(1+\frac{r}{4} )^{40}

          Take root 40^{th} root on both side,

                                                         \sqrt[40]{2} = (1+\frac{r}{4} )

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                                     (1.017479692)(4) = (r+4)

                                                  4.06992=(r+4)

                                                              r = 4.06992 -4

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Result:

             The interest rate is 6.992%, if a bank advertises that it compounds money quarterly and that it will take Double your money in 10 years.

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