if you have 3 gallons of 95% alcohol, how much pure water should be added to be able to produce 70% alcohol?

 Approximately 1.0714 gallons

Work Shown:

x = amount of pure water

3 gallons of 95% alcohol means you have 3*0.95 = 2.85 gallons of pure alcohol.

If we add on x gallons of pure water, we'll have 3+x gallons of solution

So we'll have 2.85/(3+x) representing the ratio of the amount of pure alcohol to total solution. Set this equal to 0.70 and solve for x

2.85/(3+x) = 0.70

2.85 = 0.70(3+x)

2.85 = 0.70(3)+0.70(x)

2.85 = 2.10+0.70x

2.85-2.10 = 0.70x

0.75 = 0.70x

0.70x = 0.75

x = 0.75/0.70

x = 1.07142857142858 which is approximate

x = 1.0714

So if you add about 1.0714 gallons of pure water, you'll go from 95% alcohol to 70% alcohol.

whatare you sayig

step-by-step explanation:

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

~