how much pure water must be mixed with 8 pints of 70% developer to produce a mixture that is 13%?

Answer 1

let x be the amount of pure water added to the mixture.

In 8 pints, water is 30% i.e. 2.4 pints
Total water 2.4+x pints in new mixture

By adding x pint water the mixture becomes 8+x pints
In new mixture developer is 13% and water is 87%
In this mixture water is (8+x)*87/100 pints

Therefore 2.4+x = (8+x)*87/100
or 2.4+x = 6.96 +0.87x
or x-0.87x = 6.96 - 2.4 = 4.56
or 0.13x = 4.56
or x = 4.56/0.13 = 456/13 = 35.08 approx.

This can also be solved as follows:-

2.4 : 2.4+x :: 30%:87% or 30:87

2.4*30 = (2.4+x)*87
Now solve for x

Answer 2

You can also use a Pearson square. Pure water has 0% developer.

Draw a box, write the mixing values on the left hand side and desired percent in the middle.

0---------------

.........13

70-------------

(Sides of the box are not drawn)

go diagonally, subtract and write the answers in the opposite corner

13-0=13
70-13=57

The box looks like:

0--------------- 57

...........13

70------------- 13

add the right side of the box 57+13=70

Water will be 57/70 of the total
Developer will be 13/70 of the total

let T be the total amount of the mixture

we are told (13/70) T=8
Solve for T
T = 8*(70/13)

The amount of water is 57/70T
Substitute T in

57/70 *8*(70/13)

8*57/13

A little more than 35 pints

Answer 3

The developer solution is 70%, so there are 70% of 8 pints of developer in it. 7/10*8 = 5.6
5.6 is 13% of what? 560/13 = 43 1/13.
Take away the original 8 pints, that leaves 35 1/13 pints that need to be added.

Answer 4

13% developer right?

let x be the amount of pure water added

there are 8 pints. 0.7(8) = 5.6 pints are developer. That means 8 - 5.6 = 2.4 pints are water

after adding x amount of pure water, the will be the total of
x + 8, in which 87% are WATER

2.4 + x = .87(x + 8)
2.4 + x = .87x + 6.96
.13x = 4.56
x =~ 35.077 pints of pure water <== answer

Answer 5

Let x be the number of pints of water to add

some 30% water + some 100% water = some 87% water
.3*8 + x = .87(x+8)
2.4 + x = .87x + 6.96
.13x = 4.56
x = 35.1 pints of pure water

Answer 6

70% developer Water=30%=0,3*8 pint=2,4pint

13% developer Water =87%=87/30%2,4 pint~6 pint





























30/13*2,4pint=2,248*2,4Pint=5,3952 pint