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So the total number of nails is 650, therefore:

  • X + Y = 650, and 5X + 7Y = 4350

First we can solve the first equation for Y:

  • Y = 650-X

Now that we know the relationship between X and Y, we can solve for one of them by substituting that value into the other equation. :

  • 5X + 7Y = 4350
  • 5X + 7(650-X) = 4350
  • 5X + 4550 - 7X = 4350
  • -2X + 4550 = 4350
  • -2X=-200
  • X=100

Since Y = 650-X, Y = 550.

If we plug those numbers into our original equations then we can verify the solution:

7(550) + 5(100) = 4350.

(550) + (100) = 650

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Michael Scalise

Lvl 12
3y ago

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Q: A mixture of 650 nails costs $43.50. If some of the nails cost 5 cents a piece, and therest costs 7 cents a piece, how many of each are there?
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