A Shipment Of TV Sets, Some Weighing 30 Kg Each And The Others Weighing 50 Kg Each Has A Total Weight Of 880 Kg. If There Are 20 TV Sets All Together, How Many Weigh 50 Kg?

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Oddman Profile
Oddman answered
Let H be the number of heavy (50 kg) TV sets, and L be the number of lighter (30 kg) TV sets.

The total weight of all TV sets is  880 kg = (50 kg)*H + (30 kg)*L.
The total number of all TV sets is  20 = H + L.

We have 2 equations in 2 unknowns. This gives enough information to solve for H and L. Let's do it this way: Multiply the second equation by 30 and subtract it from the first. (Note we will drop the use of the kg units for this.)

(880) - 30(20) = (50H + 30L) - 30(H + L)
880 - 600 = 50H - 30H + 30L - 30L    (use the distributive property)
280 = 20H    (collect terms)
14 = H    (divide both sides by 20)

14 sets weigh 50 kg.
_____
20 = 14 + L    (put the value of H into the second equation)
6 = L    (subtract 14 from both sides)

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