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...
Assuming the solid likes are the design. So we see two parallelograms there.
Area of 1 parallelogram = base x height. Since we have a joint height, we will multiply the total height with the base (both have the same base length) to get the area of 1 design.
You can use soh cah toa. Basically you pic one side and if the interior angle is opposite or next to it, you you soh, or cah, or toa, it's based on where the angle is.
