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In 2016 Alphonse grew twice the number of grapes that Pierre did. In 2017 Pierre grew twice the number of grapes that Alphonse did. Over the two years Alphonse grew 49000 grapes which was 7600 less than Pierre. How many grapes did Alphonse grow in 2016?

Sep 11, 2017

#1
+96246
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Let x be the number of grapes that Pierre grew in 2016.......then 2x  was the number that Alphonse grew that year

And let y be the number of grapes that Alphonse grew in 2017.....then  2y was the number that Pierre grew that year

So  we have that

2x  + y  = 49000    =     number of grapes that Alphonse grew over the two years

x +  2y  =  49000 + 7600  =  number of grapes that Pierre grew over the two years

Simplify

2x  +  y  =  49000

x  +  2y   = 56600

Multiply the 1st equation by  -2   and we have

-4x -  2y       =     -98000

x +  2y       =      56600        add these equations

-3x  = -41400      divide both sides by -3

x  =  13800

And Alphonse grew twice as many in 2016  = 27600

Sep 11, 2017
#2
+1

Thank you so much, I looked at this 20 mins before it was due in. Whew.

Guest Sep 13, 2017