My production line creates 3 different widgets. Widget A sells for $12. Widget B sells for $18. Widget C sells for $35. I made a total revenue of $1735 yesterday. I sold a total of 70 widgets. The number of C widgets sold is equal to the total number A and B sold. How many of each type of widgets did I sell?

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Step-by-step explanation:

Half the widgets sold were $35 widgets, so the revenue from them was ...

  (70/2)($35) = $1225

This means the remaining $1735 -1225 = $510 in revenue came from the sale of a total of 35 A and B widgets.

If we let 'b' represent the number of B widgets sold, then the revenue is ...

  12(35 -b) + 18b = 510

  6b +420 = 510

  6b = 90

  b = 15 . . . . . . . number of B widgets sold

  35 -b = 20 . . . number of A widgets sold

20 A widgets, 15 B widgets, and 35 C widgets were sold.

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Check

Total revenue was 20(12) +15(18) +35(35) = 240 +270 +1225 = 1735.

Total widgets were 20 +15 +35 = 70.

The total of A and B was 20 +15 = 35, the same as the number of C.

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step-by-step explanation:

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