Question 192154
Let x, y, and z be the number of books in piles 1, 2, and 3.



Since there are "3000 books in three piles", this means that {{{x+y+z=3000}}}



Because " Pile 1 has 10 more books than pile 2", this tells us that {{{x=y+10}}}



Also, since "Pile 2 has twice as many as pile 3", this gives the equation {{{y=2z}}}




{{{x+y+z=3000}}} Start with the given equation



{{{(y+10)+y+z=3000}}} Plug in {{{x=y+10}}}



{{{2z+10+2z+z=3000}}} Plug in {{{y=2z}}}



{{{10+5z=3000}}} Combine like terms on the left side.



{{{5z=3000-10}}} Subtract {{{10}}} from both sides.



{{{5z=2990}}} Combine like terms on the right side.



{{{z=(2990)/(5)}}} Divide both sides by {{{5}}} to isolate {{{z}}}.



{{{z=598}}} Reduce. So there are 598 books in the third pile


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{{{y=2z}}} Go back to the third equation



{{{y=2(598)}}} Plug in {{{z=598}}}



{{{y=1196}}} Multiply. So there are 1,196 books in the second pile



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{{{x=y+10}}} Go back to the first equation



{{{x=1196+10}}} Plug in {{{y=1196}}}



{{{x=1206}}} Add. So there are 1,206 books in the first pile.




To check the answers, simply add up the books to get 3,000.