SOLUTION: pls answer with complete solution! very important! 1. A water tank has two valves, A and B. When only valve A is open, the tank is emptied in 6 hours. Furthermore, it takes t

Question 205076: pls answer with complete solution! very important!

1. A water tank has two valves, A and B. When only valve A is open, the tank is emptied in 6 hours. Furthermore, it takes twelve hours to empty the tank if only valve B is open. How long will it takes to empty the tank if both valves are open?

2. The sysfies organized a benefit show for their JS prom. They sold $25,$50, and $100 tickets. The $25-ticket sales was twice as many as the $100-ticket while the $50-ticket was 50 more than the $100 tickets. How many of each kind of ticket were sold if the total sales was $22,500?

3. An 8-liter solution is 25% alcohol. How much water must be added to reduce the concentration of alcohol in the solution to 20%?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
1. A water tank has two valves, A and B. When only valve A is open, the tank is
emptied in 6 hours. Furthermore, it takes twelve hours to empty the tank if
only valve B is open. How long will it takes to empty the tank if both valves are open?
:
let t = time required when both valves are open
:
let the completed job (empty tank) = 1
+ = 1
multiply equation by 12 to get rid of the denominators, results
2t + t = 12
3t = 12
t =
t = 4 hrs working together
;
you can check solution by substituting 4 for t in the original equation
:
:
;
2. The sysfies organized a benefit show for their JS prom. They sold $25,$50,
and $100 tickets. The $25-ticket sales was twice as many as the $100-ticket
while the $50-ticket was 50 more than the $100 tickets.
How many of each kind of ticket were sold if the total sales was $22,500?
:
let x, y, z = 25, 50, $100 tickets respectively
:
Total sales equation:
25x + 50y + 100z = 22,500
:
"the $25-ticket sales was twice as many as the $100-ticket"
x = 2z
:
"the $50-ticket was 50 more than the $100 tickets"
y = z + 50
:
Substitute 2z for x, and (z+50) for y, in the total sales equation, find z
25(2z) + 50(z+50) + 100z = 22500
50z + 50z + 2500 + 100z = 22500
200z = 22500 - 2500
200z = 20000
z =
z = 100 ea $100 ticket sold
:
You can find x & y using the equations we have for x and y
;
;
3. An 8-liter solution is 25% alcohol.
How much water must be added to reduce the concentration of alcohol in the solution to 20%?
:
Let x = amt or water required
.25(8) = .20(x+8)
2 = .2x + 1.6
2 - 1.6 = .2x
.4 = .2x
x =
x = 2 liters of water required
;
Check solution:
.25(8) = .2(2 + 8)
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