### Math Notes

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#### Algebra Solutions

##### Topics || Problems

How much copper and how much iron should be added to 100 pounds of an alloy containing 25% copper and 40 % iron in order to obtain an alloy containing 30% copper and 50% iron. Solution:
 M 1 M 2 M 3 Resulting Mix Copper $$25 \%$$ $$100 \%$$ $$0 \%$$ $$30 \%$$ Iron $$40 \%$$ $$0 \%$$ $$100 \%$$ $$50 \%$$ Weight in lbs $$100$$ $$x$$ $$y$$ $$100+x+y$$

$$0.25(100)+x=0.3(100+x+y)$$

$$25 +x = 30 +0.3x +0.3y$$

$$0.7x = 5 +0.3y$$

$$x = \frac{50}{7} +\frac{3y}{7}$$

$$0.4(100)+y=0.5(100+x+y)$$

$$40 +y= 50 +0.5x +0.5y$$

$$-10+0.5y = 0.5x$$

$$-20 + y = x$$

$$-20+y = \frac{50}{7} +\frac{3y}{7}$$

$$y =47.5 \text{lbs}$$

$$x = 47.5-20 = 27.5 \text{lbs}$$

Answer: the weight of the copper is 27.5 lbs and the iron is 47.5 lbs