Answer:
a) 4 months
b) $600
Step-by-step explanation:
1. x - number of months the total amount paid to be the same for both stores.
2. That same amount for store A: 
3. That same amount for store B: 
4. Since it's the same amount for both stores we can make an equation:
5. To find that same amount, we can use either side of above equation:
Answer:
60.
Step-by-step explanation:
This is a permutation exercise because order matters. The formula is n!/(n-r)!. In this case n=5 and r=3 so,
5!/(5-3)! = 5!/2! = 5!/2 = (5*4*3*2*1)/2 we can simplify the 2 and obtain 5*4*3= 60.
X= # gallons of pure water that should be evaporated
The total amount of salt must be equal before and after evaporation.
STEP 1
BEFORE EVAPORATION: multiply the percent of salt in the solution before evaporation by the total gallons of solution
= 12% * 160 gallonsconvert 12% to decimal form (12% ÷ 100)
= 0.12 * 60
STEP 2
AFTER EVAPORATION: subtract the number of gallons of pure water that should be evaporated from the total number of gallons of the solution and multiply by the percent of salt in the solution after evaporation
= 20% * (160 - x)convert 20% to decimal form (20% ÷ 100)
= 0.20(160 - x)
STEP 3
Set the before & after evaporation equations equal to one another to solve for x.
0.12 * 160= 0.20(160 - x)multiply 0.20 by each term in parentheses
19.2= (0.20 * 160) + (0.20 * -x)multiply in parentheses
19.2 = 32 - 0.20xsubtract 32 from both sides
-12.8= -0.20xdivide both sides by -0.20
64 gallons= x
CHECK:substitute x= 64 into the step 3 equation
0.12 * 160= 0.20(160 - x)19.2= 0.20(160 - 64)subtract in parentheses19.2= 0.20(96)19.2= 19.2
ANSWER: 64 gallons of pure water should be evaporated.
Hope this helps! :)
