Bronze is an alloy that is made of zinc, tin, and copper in a specified proportion. Suppose an order is placed for 1000 pounds of bronze. The amount of tin in this order of bronze is two times the amount of zinc, and the amount of copper is 10 pounds more than 15 times the amount of tin. Find the number of pounds of zinc, tin, and copper.
z + t + c = 1000
t = 2 z
c = 15 t + 10 = 30 z + 10
z + 2z + 30z + 10 = 1000
solve for z, then substitute back to find c and t
To find the number of pounds of zinc, tin, and copper in the 1000-pound order of bronze, we can set up a system of equations based on the given information.
Let's use the following variables:
Z = pounds of zinc
T = pounds of tin
C = pounds of copper
Based on the information given, we know that:
1) The amount of tin in the order is two times the amount of zinc: T = 2Z
2) The amount of copper in the order is 10 pounds more than 15 times the amount of tin: C = 15T + 10
Since the total weight of the order is 1000 pounds, we can also write an equation relating the weights of zinc, tin, and copper:
Z + T + C = 1000
Now, we can substitute the values we obtained from equations (1) and (2) into the third equation to solve for the variables:
Z + T + C = 1000
Z + 2Z + (15T + 10) = 1000 [substituting T = 2Z and C = 15T + 10]
3Z + 15T + 10 = 1000
3Z + 15(2Z) + 10 = 1000 [substituting T = 2Z]
3Z + 30Z + 10 = 1000
33Z + 10 = 1000
33Z = 1000 - 10
33Z = 990
Z = 990/33
Z = 30
Now that we have the value of Z (pounds of zinc), we can substitute this value back into equation (1) to find T (pounds of tin):
T = 2Z = 2(30) = 60
Finally, we can substitute the values of Z and T into equation (2) to find C (pounds of copper):
C = 15T + 10 = 15(60) + 10 = 900 + 10 = 910
Therefore, the number of pounds of zinc is 30, the number of pounds of tin is 60, and the number of pounds of copper is 910.