Question

(75 points) ASAP 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 in the boxes.

Answer 1

50 grams of 45% alloy and 50 grams of tin alloy

Explanation:

Those are the two equations:

x+y=100

the sum of the weight of both alloys is 100 g

0.5x+0.45y=0.25*100

the sum of the weights of tin has to be 25% of 100g, which is actually 25 g

0.5x+0.45y=25

So we have:

x+y=100

0.5x+0.45y=25

x=10-y

0.5x+0.45y=25

We substitute:

0.5(10-y)+0.45y=25

We calculate:

5-0.5y+0.45y=25

-0.5y+0.45y=20

0.4y=20

4y=200

y=50

So he needs 50 grams of 45% alloy and 100-50=50 grams of tin alloy as well

Answer 2

Here x is the number of grams of the 5% tin alloy and y is the number of the 45% tin alloy,

Since, x gram and y gram is mixed to obtain 100 gram of alloy,

⇒ x + y = 100 --------(1)

Also, in the resultant alloy there is 25 % of tin,

Thus, 5% of x + 45% of y = 25% of 100

⇒ 5 x + 45 y = 2500

⇒ x + 9 y = 500 ------(2)

Equation (1) - Equation (2),

- 8 y = - 400

y = 50

By putting the value of y in equation (1),

We get , x = 50

Therefore, 50 gram of alloy that is 5% tin is mixed with 50 gram of alloy that is 45% tin for obtaining 100 gram of alloy that is 25% of tin.