Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks . Wayne is building bookshelves to sell at a furniture storeFirst, he built 10 small bookshelves and 6 large bookshelves, using a total of 638 nails. Later, he built 10 small bookshelves and 9 large bookshelves, using a total of 797 nails. How many nails does Wayne use to build the shelves? nails to make each small bookshelf and nails to make Wayne uses each large one .
Let x be the number of nails to make each small bookshelf and y be the number of nails to make each large bookshelf.
The first equation representing the total number of nails used for the first set of bookshelves is:
10x + 6y = 638
The second equation representing the total number of nails used for the second set of bookshelves is:
10x + 9y = 797
To solve this system of equations using elimination, we can multiply the first equation by 3 and the second equation by -2 to eliminate x:
30x + 18y = 1914
-20x - 18y = -1594
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10x = 320
Therefore, x = 32
Plugging back x into one of the original equations:
10(32) + 6y = 638
320 + 6y = 638
6y = 318
y = 53
Therefore, Wayne uses 32 nails to make each small bookshelf and 53 nails to make each large one, using a total of 638 + 797 = 1,435 nails to build the shelves.