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# mathematics

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Isaac is building bookshelves to sell at a furniture store. First, he built 4 small bookshelves and 3 large bookshelves, using a total of 282 nails. Later, he built 5 small bookshelves and 3 large bookshelves, using a total of 315 nails. How many nails does Isaac use to build the shelves?

Apr 20, 2021

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By "How many nails does Isaac use to build the shelves", you could mean the total amount or the amount for each type fo shelve, so I'll try and answer both.

The total nails are not too hard to figure out, it's just simple addition, so: 282 + 315 = 597 total nails

Now, for the harder question, how many nails does Isaac need to build each shelve type? We can figure this out by using simple algebra.

4 small shelves and 3 large shelves use 282 nails.

5 small shelves and 3 large shelves use 315 nails.

4x + 3y = 282

5x + 3y = 315

Using a simple system of equations tactic, you can figure out that the answer needed is:

33 nails for small shelves

and

50 nails for large shelves.

To prove that this is correct, we can input the answers into the system, getting:

4 (33) + 3 (50) = 282    (Correct)

and

5 (33) + 3 (50) = 315    (Correct)

So, Isaac needs 33 nails for small shelves and 50 nails for large shelves.

Apr 20, 2021