Question 1203490
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This problem can be worked using a formal algebraic method, as shown in the response from tutor @ikleyn.<br>
It can also be solved quickly and easily by an informal method using the ratios of the two ingredients in the mixture.<br>
The trophy is 8% motrium; sornog contains 0% motrium while yotril contains 12% motrium.<br>
On a number line, 8% is two-thirds of the way from 0% to 12%.  That means 2/3 of the mixture for the trophy is yotril; that in turn means there is 2 times as much yotril as sornog in the trophy alloy.<br>
Now use that same idea of percentages on a number line to find the percentage of gold in sornog.<br>
The percentage of gold in sornog is not known; call it x%.  The percentage of gold in yotril is 75%; the percentage of gold in the trophy alloy is 72%.  Since 2/3 of the trophy alloy is yotril, the calculation we need to do to find x is this:<br>
72% is 2/3 of the way from x% to 75%<br>
Use formal algebra or logical reasoning and simple arithmetic to find that the percentage of gold in sornog is 66%.<br>