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Gelneren [198K]
3 years ago
15

19 = 15 w- 4(3 w-1) solve for w

Mathematics
1 answer:
Gnom [1K]3 years ago
8 0

Step-by-step explanation:

Simplifying

19 = 15w + -4(3w + -1)

Reorder the terms:

19 = 15w + -4(-1 + 3w)

19 = 15w + (-1 * -4 + 3w * -4)

19 = 15w + (4 + -12w)

Reorder the terms:

19 = 4 + 15w + -12w

Combine like terms: 15w + -12w = 3w

19 = 4 + 3w

Solving

19 = 4 + 3w

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '-3w' to each side of the equation.

19 + -3w = 4 + 3w + -3w

Combine like terms: 3w + -3w = 0

19 + -3w = 4 + 0

19 + -3w = 4

Add '-19' to each side of the equation.

19 + -19 + -3w = 4 + -19

Combine like terms: 19 + -19 = 0

0 + -3w = 4 + -19

-3w = 4 + -19

Combine like terms: 4 + -19 = -15

-3w = -15

Divide each side by '-3'.

w = 5

Simplifying

w = 5

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3 years ago
Letang Industrial Systems Company (LISC) is trying to decide between two different conveyor belt systems. System A costs $280,00
Vanyuwa [196]

We have to calculate the EAC for both the conveyor belt system.

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<u>Equivalent Annual Cost or (EAC) for the SYSTEM-A</u>

$\text{Operating cash flow } = \text{Pre-tax annual operating cost (1-tax rate )} + (\text{depreciation expense} \times $tax rate )

                                $=-855,000(1-0.23)+\left[\left(\frac{280,000}{4}\right)\times 0.23\right]$

                               $= (-85,000 \times 0.77 ) + (70,000 \times 0.23)$

                               = $ 49,350

Year      Annual Cost flow     Present value factor    Present Value of Annual

                                                     at 10%                              cash flow

1                    -49,350                  0.909091                          -44,863.64

2                  -49,350                   0.826446                          -40,785.12

3                   -49,350                  0.751315                            -37,077.39

4                   -49,350                 <u> 0.683013   </u>                       <u>-33,706.71  </u>

     Total                                    $ 3.169865                       $ -156,432.86  

Therefore, Net Present value = present value of the annual cash flow - initial investment.

           = 156,432.86 - 280,000

          = $ 436,432.86 (negative)

Now the EAC or the Equivalent Annual Cost for System A :

$\text{EAC}= \text{Net present value / (PVIFA 10 percent, 4 years)}$

        $=\frac{436,432.86}{3.169865}$

        $= 137,681.86 $ dollar (negative)

$\text{Operating cash flow } = \text{Pre-tax annual operating cost (1-tax rate )} + (\text{depreciation expense} \times $tax rate)

$=79,000(1-0.23)+\left[\left(\frac{360,000}{6}\right) \times 0.23\right]$

$=(-78,000 \times 0.77)+(60,000 \times 0.23)$

= -$ 47,030

Year      Annual Cost flow     Present value factor    Present Value of Annual

                                                     at 10%                              cash flow

1                    -47,030                  0.909091                          -42,754.55

2                  -47,030                   0.826446                          -38,867.77

3                   -47,030                  0.751315                           -35,334.34

4                   -47,030                 0.683013                            -32,122.12

5                  -47,030                  0.620921                            -29,201.93

6                  -47,030                 <u> 0.564474  </u>                        <u>  -26,547.21 </u>  

    Total                                     $ 4.355261                       $  -204,827.91

Net Present Value = Present Value of annual cash inflows – Initial Investment

$= 204,827.91 - 360,000$

= -$ 564,827.91 (negative)

EAC for system B:

Equivalent Annual Cost for system B $=\frac{\text{net present value}}{\text{PVIFA 10 \text percent, 6 years}}$

$=\frac{-564,827.91}{4.355261}$

= -$129,688.66 (negative)

7 0
2 years ago
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