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Use a system of equations to solve this problem.
Bronze is a mix, or alloy, of tin and copper. A metal worker needs 100 g of bronze that is 25% tin. He has one tin/copper alloy that is 5% tin and another tin/copper alloy that is 45% tin.
Let x = the number of grams of the 5% tin alloy.
Let y = the number of grams of the 45% tin alloy.
How many grams of each alloy should the metal worker combine?
Enter your answers into the boxes.
__g of the 5% tin alloy and __g of the 45% tin alloy.

Respuesta :

cdw2014

He needs a total of 100 g of bronze. If 25% needs to be tin, that means he needs 25 g of tin between the two alloys.

So 0.05x + 0.45y = 25 will tell us how much of each alloy we need to get 25 g of tin.

And x + y = 100 tells us that the total amount of bronze is 100 g.

Solve the second equation for x.

x = 100 - y

Now plug 100 - y into the first equation for x:

0.05(100-y) + 0.45y = 25

5 - 0.05y + 0.45y = 25

5 + 0.4y = 25

0.4y = 20

y = 50

Now plug y back into either of the original equations to find x.

x + 50 = 100

x = 50

The answer is 50 g of both alloys.







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