Ametal worker has several 1-kilogram bars of a metal alloy that contain 23% copper and several 1-kilogram bars that contain 79% copper. how many bars of each type of alloy should be melted and combined to create 48 kilograms of a 44% copper alloy?

Step-by-step

Difference         21%                                         35%

          |||

        23%                              44%                                                  79%

The ratio of 23% alloy to 79% alloy is given as

23% : 79% = 35 : 21 = 5:3

(see above diagram)

So weight of each alloy is given by:

23% alloy = 5/(5+3) * 48 kg = 30 kg

79% alloy = 3/(5+3) * 48 kg = 18 kg

Check:

total weight = 30+18 kg = 48 kg

Total weight of copper in 48 kg of 44% alloy = 48*0.44 = 21.12 kg

Total weight of copper of mixed alloys= 30*0.23 + 18*0.79 = 21.12 kg (checks)

∠cbe and ∠deb are same-side interior angles.

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