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 $22.95
5. Let M represent number of months. 3.5m + 90 = 132 3.5m + 90 - 90 = 132 - 90 3.5m = 42 (1/3.5)(3.5m) = (1/3.5)(42) m = 12, the boy will grow 132cm tall, 12 months from now
6. Let N represent given number n + 1/6n + (2 1/2)n + 7 = 12 1/2 n ( 1 + 1/6 + 5/2) + 7 = 12 1/2 n(6/6 + 1/6 + 15/6) + 7 = 12 1/2 n(22/6 + 7 - 7 = 12 1/2 11/3n + 7 - 7 = 12 1/2 - 7 11/3n + 0 = 5 1/2 11/3n = 5 1/2 3/11.11/3 = 3/11.11/2 1n = 3/2 n = 1 1/2, is the number
7. let X represents the first number, then 33 - x represents the other # since their sum is 33 X - (33 - x) = 2 X + ( - (33 - x)) = 2 X + ( -33) + X = 2 2x + (- 33) = 2 2x + (- 33) + 33 = 2 + 33 2x + 0 = 35 1/2 * 2x = 1/2 * 35 1x = 35/2 x = 17 1/2
33 - x = 33 - (17 1/2) = 15 1/2 {17 1/2, 15 1/2}
8. Let T represents number of tokens in machine A. Then 1/2T represents the number of tokens in machine B, and 3/4T represents the number of tokens in machine C.
T + 1/2T + 3/4T = 18,324 9/4T = 18, 324 T = 8, 144 Machine A took 8,144T, Machine B 4,072T, Machine C 6,108T
9. Let Z represents the cost of a pencil in dollars. Then, the cost of a pen in dollars is Z + 0.11
Faster car average speed is 58mph Slower car average speed is 51mph
Distance = rate * time d = 51 * 5 1/2 d = 51 * 11/2 d = 280.5
Slower car travel 280.5 miles in 5 1/2hrs d = 58 * 5 1/2 d = 58 * 11/2 d = 319 or 599.5 - 280.5 = 319
Faster car travel 319 miles in 5 1/2 hrs
The slower car travels 280.5 miles in 5 1/2hrs. remainder of trips for both vehicle is 38.5 miles, because, 319 - 280.5 = 38.5
distance = rate * time 38.5 = 51 (t) 1/51(38.5) = 1/51(51)(t) 38.5/51 = 1t 77/102 = t, This time is in hours. To convert to minutes, multiply by 60 minutes per hour 77/102 * 60 = 77/51 * 30 = 2310/51 = 45, The slower car will arrive at about 45 minutes after the first car.
Hope this helps!!!
Next time please ask for help in chunks!! Try for yourself.. this is a lot...
starting amount * (1. interst rate) ^ number of years
example if you have 100$ and you want to know how much it is worth if it appretiates by 7% of a period of 20 years it would look something like this;
100 * (1.10) ^20 = 672.74$
but since you have to figure out what it was in 2008 which was exactly half way in the period you divide the exponent by half so your formula should be;
I know the answer is right because I asked my teacher and it's correct.
