Answer:
$450
Step-by-step explanation:
Let E be the amount of money Ethan starts with, J be the amount Jun Wei starts with, and R be the amount Raj starts with. Let M be the total amount of money to start with.
To start:
![E:J:R = 5:6:9](https://tex.z-dn.net/?f=E%3AJ%3AR%20%3D%205%3A6%3A9)
This means Ethan has 5/20 of M, the money to start with. This reduces to 1/4 of M.
Afterwards:
![(E-50):J:R = 3:4:6](https://tex.z-dn.net/?f=%28E-50%29%3AJ%3AR%20%3D%203%3A4%3A6)
This means Ethan has 3/13 of the remaining money (which is M-50!) after giving up 50. So
E = (M/4), or 4E = M
and
![(E - 50) = 3/13 * (M - 50)](https://tex.z-dn.net/?f=%28E%20-%2050%29%20%3D%203%2F13%20%2A%20%28M%20-%2050%29)
We know 4E = M, so we can substitute that in:
![(E - 50) = 3/13 * (4E - 50)E - 50 = (12/13)E - 150/13E - 650/13 = (12/13)E - 150/13(1/13)E = 500/13E = 500](https://tex.z-dn.net/?f=%28E%20-%2050%29%20%3D%203%2F13%20%2A%20%284E%20-%2050%29E%20-%2050%20%3D%20%2812%2F13%29E%20-%20150%2F13E%20-%20650%2F13%20%3D%20%2812%2F13%29E%20-%20150%2F13%281%2F13%29E%20%3D%20500%2F13E%20%3D%20500)
That's how much money Ethan had to start with. But we're asked how much he has AFTER giving $50 away, so that's $450.
Answer:
$203.00
Step-by-step explanation:
Since the bank in question compounds interest just once, and this is a one year investment, it can be treated as a simple rate interest problem. Therefore, the total balance after one year (B) is given by the following formula:
![B= 200*(1+i)\\B= 200*(1+0.015)\\\\B= 203](https://tex.z-dn.net/?f=B%3D%20200%2A%281%2Bi%29%5C%5CB%3D%20200%2A%281%2B0.015%29%5C%5C%5C%5CB%3D%20203)
April's balance would be $203.00 after one year.
First we list the multiples of each number.
multiples of 5 are 10,15,20,25,30,35,40,...
multiples of 6 are 12,18,24,30,36,42,48,...
multiples of 15 are 30,45,60,75,90,...
now, when you look at the list of multiples, you can see that 30 is the smallest number that appears in each list.
therefore, the least common multiple of...... 5,6 and 15 is 30.
9514 1404 393
Answer:
- |w -30| > 1.6
- (-∞, 28.4) U (31.6, ∞)
Step-by-step explanation:
1. The snack bags will be rejected if their weight differs from 30 grams by more than 1.6 grams:
|w -30| > 1.6
__
2. This inequality resolves to two inequalities.
w -30 > 1.6
w > 31.6 . . . . . add 30
and
-(w -30) > 1.6
w -30 < -1.6 . . . multiply by -1
w < 28.4 . . . . . add 30
The solution in interval notation is the union of the two disjoint intervals:
(-∞, 28.4) U (31.6, ∞)
Remember the formula for calculating volume is: Volume = Area by height. V = A X h.