Question 1165719
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(1) A typical setup using formal algebra....<br>
50g of 10% acid, plus x g of 100% acid, equals (50+x) g of 20% acid:<br>
{{{.10(50)+1.00(x) = .20(50+x)}}}<br>
Solve using basic algebra.<br>
(2) A quick and easy way to solve ANY 2-part mixture problem like this....<br>
Look at the three percentages 10, 20, and 100 on a number line and see where the 20% is in relation to the 10% and 100%.<br>
The 20% is 1/9 of the way from 10% to 100%.  (From 10 to 100 is a difference of 90; from 10 to 20 is a difference of 10; 10/90 = 1/9.)<br>
That means 1/9 of the mixture must be the added 100% acid.<br>
So the 50g of 10% acid is 8/9 of the mixture; 1/9 of the mixture is then 1/8 of 50g, or 6.25g.<br>
ANSWER: 6.25 grams of 100% acid.<br>
CHECK:
.10(50)+1.00(6.25) = 5+6.25 = 11.25
.20(50+6.25) = .20(56.25) = 11.25<br>