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Ira Lisetskai [31]
3 years ago
14

(SHOW WORK NEED IT BY TONIGHT! )Write a system of equations to describe the situation below, solve using substitution, and fill

in the blanks.
Nick, a caterer, is investing some money in equipment and employees to help grow his business. Recently he spent $47 on equipment and hired a server who makes $15 per hour. Nick is hoping to make up these expense at the next job that is scheduled, which pays a base of $54 in addition to $14 per hour that the server works. In theory, this event could pay enough to cancel out Nick's expenditures. How much would the job pay? How long would the job have to be?



The expenditures and pay would both be $_ if the job lasted for _ hours.
Mathematics
1 answer:
earnstyle [38]3 years ago
8 0

Let X = the number of hours the server works.

The equation for the amount Nick spends is 15x + 47

The next job pays 14x + 54

Set the equations to equal and solve for x:

15x + 47 = 14x +54

Subtract 14x from both sides:

X + 47 = 54

Subtract 47 from both sides:

X = 7

Now replace x with 7 in the second equation:

14x + 54 = 14(7) + 54 = 98 +54 = 152

The job would pay $152 and be 7 hours long.

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Donna de paul is raising money for the homeless. She discovers that each church group requires 2 hours of let her writing and 1
Salsk061 [2.6K]

Answer:

x  =  7

y  =  3

z (max)  =  4950/3  =  1650

Step-by-step explanation:

Let call  

x numbers of church goup and

y numbers of Union Local

Then  

First contraint

2*x + 2*y ≤ 20

Second one

1*x + 3*y ≤ 16

Objective Function

z = 150*x + 200*y

Then the system is

z = 150*x + 200*y To maximize

Subject to:

2*x + 2*y ≤ 20

1*x + 3*y ≤ 16

x ≥ 0 y ≥ 0

We will solve by using the Simplex method

z - 150 *x - 200*y = 0

2*x + 2*y + s₁ = 20  

1*x + 3*y + 0s₁ + s₂ = 16

First Table

z           x          y          s₁           s₂          Cte

1        -150    -200       0            0     =      0

0          2         2           1            0     =    20

0          1          3          0            1      =     16

First iteration:

Column pivot   ( y column ) row pivot (third row) pivot 3

Second table

z           x                y          s₁           s₂                Cte

1       -250/3           0          0         200/3    =    3200/3

0      - 4/3               0          -1           2/3       =    -20/3

0         1/3               1            0           1/3       =    -20/3

Second iteration:

Column pivot  ( x column ) row pivot  (second row)  pivot  -4/3

Third table

z           x                y          s₁           s₂                Cte

1            0               0      750/12    700/6    =   4950/3

0            1                0        3/4          -1/2     =    7

0            0                1         -1/4          1/2     =  9/3

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Step-by-step explanation:

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The correct answer is 13
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Translate this problem to an equation and solve. The area of a patio is 72 square feet. The length of the patio is 1 foot longer
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A = LW
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72 = W(W + 1)
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