Question 544137
To make a mixture that is 25% betadine, how many gallons of 100% pure betadine need to be mixed with 10 gallons of 15% betadine solution?
:
let x = amt 100% stuff required to accomplish this
:
A typical mixture equation, use the decimal equiv of percent
:
1.00x + .15(10) = .25(x+10)
1x + 1.5 = .25x + 2.5
1x - .25x = 2.5 - 1.5
.75x = 1
x = {{{1/.75}}}
x = 1{{{1/3}}} gal of 100% stuff required
:
:
Check our solution in the original mixture equation
1.333 + 1.5 = .25(1.333+10)
1.8333 = .25(11.333)
1.8333 = 1.833, equality reigns, so it checks out