Q:

Please help me with #1. I need an equation and the number of years.

Accepted Solution

A:
1. 12000(1 - n/5) = 2,400
     12000 - 2400n = 2400
      - 2400n + 12000 - 12000 = 2400 - 12000
      - 2400 = - 9600
             n = 4, After 4 years the scanner will be replaced.



2.  Let x represents Michael age in years now.
     
                            
                          Now           4years later  
                            
Michael                 x                 x + 4

      
John                      x - 17           (x - 17) + 4


                              x + 4 + x - 17 + 4 = 49
                               x + 4 + x - 13 = 49
                                2x - 9 = 49
                                 2x - 9 + 9 = 49 + 9
                                            2x = 58
                                     (1/2)(2x) = (1/2)(58)
                                                x = 29, Michaels age is 29


3. Brady speed 1   Rate(mph)       Time(hours)           Distance(miles)
                                17                     t                               17 t
     Brady speed 2    22                     4 - t                         22(4 - t)total distance

The total distance he rode  17t + 22(4 - t) = 70

The total distance = 70 miles


                                         showing work:  
                                           17t + 22(4 - t) = 70
                                            17t + 88 - 22t = 70
                                             - 5t + 88 = 70
                                              - 5t + 88 - 88 = 70 - 88
                                               - 5t  = - 18
                                                t = 3.6, Brady rode 17(mph) for 3.6(hrs).


4. t = the price of 1 shirt
     4t - 39.58 = 52.22
     4t - 39.58 = 52.22 + 39.58
      4t  + 0 = 91.80
    (1/4)(4t) = (1/4)(91.80)
               t = 22.95, price of 1 shirt was $22.95


5. Let M represent number of months.
      3.5m + 90 = 132
       3.5m + 90 - 90 = 132 - 90
        3.5m = 42
    (1/3.5)(3.5m) = (1/3.5)(42)
                      m = 12, the boy will grow 132cm tall, 12 months from now



6.   Let N represent given number
         n + 1/6n + (2 1/2)n + 7 = 12 1/2
          n ( 1 + 1/6 + 5/2) + 7  = 12 1/2
          n(6/6 + 1/6 + 15/6) + 7 = 12 1/2
           n(22/6 + 7 - 7 = 12 1/2
            11/3n + 7 - 7 = 12 1/2 - 7
              11/3n + 0 = 5 1/2
              11/3n = 5 1/2
               3/11.11/3 = 3/11.11/2
                 1n  = 3/2
                    n = 1 1/2, is the number


7. let X represents the first number, then 33 - x represents the other # since their sum is 33
     X - (33 - x) = 2
      X + ( - (33 - x)) = 2
      X + ( -33) + X = 2
       2x + (- 33) = 2
        2x + (- 33) + 33 = 2 + 33
        2x + 0 = 35
        1/2 * 2x = 1/2 * 35
         1x = 35/2
          x = 17 1/2

33 - x = 33 - (17 1/2) = 15 1/2
                     {17 1/2,  15 1/2}
                                 



8. Let T represents number of tokens in machine A. Then 1/2T represents the number of tokens in machine B, and 3/4T represents the number of tokens in machine C.

   T + 1/2T + 3/4T = 18,324
    9/4T = 18, 324
          T = 8, 144
Machine A took 8,144T, Machine B 4,072T, Machine C 6,108T



9.  Let Z represents the cost of a pencil in dollars. Then, the cost of a pen in dollars is Z + 0.11

   250(Z + Z + 0.11) = 42.5
    250(2Z + 0.11) = 42.5
    500Z + 27.5 = 42.5
    500Z + 27.5 + ( - 27.5) = 42.5 + ( -27.5)
     500Z + 0 = 15
     500Z = 15
      500Z/500 + 15/500
             Z = $0.03, a pencil costs, and  a pens cost $0.14


10. Let R represents speed in mph of faster car, Then r - 7 represents speed in mph of slow car.

 5 1/2(r) + 5 1/2(r - 7) = 599.5
  5 1/2(r + r - 7) = 599.5
 5 1/2(2r - 7) = 599.5
 11/2 (2r - 7) = 599.5
  2/11 * 11/2 (2r - 7) = 2/11 * 599.5
  1 * (2r - 7) = 1199/11
   2r - 7 = 109
   2r  - 7 + 7 = 109 + 7
   2r + 0 = 116
   2r = 116
 1/2 * 2r = 1/2 * 116
          1r = 58
             r =58

Faster car average speed is 58mph
Slower car average speed is 51mph

Distance = rate * time
 d = 51 * 5 1/2
  d = 51 * 11/2
   d = 280.5


Slower car travel 280.5 miles in 5 1/2hrs
d = 58 * 5 1/2
d = 58 * 11/2
d = 319           or  599.5 - 280.5 = 319


Faster car travel 319 miles in 5 1/2 hrs




The slower car travels 280.5 miles in 5 1/2hrs. remainder of trips for both vehicle is 38.5 miles, because, 319 - 280.5 = 38.5


distance = rate * time
38.5 = 51 (t)
1/51(38.5) = 1/51(51)(t)
38.5/51 = 1t
77/102 = t, This time is in hours. To convert to minutes, multiply by 60 minutes per hour
77/102 * 60 = 77/51 * 30 = 2310/51 = 45, The slower car will arrive at about 45 minutes after the first car.



Hope this helps!!!


Next time please ask for help in chunks!! Try for yourself.. this is a lot...