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

Question

Answer:

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...

solved

general 11 months ago 2143