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Algebra Word Problem

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a=# of grapes Aaron has
h=# of grapes Henry has
 
a+h=52
Aaron ate 11 and gave away 5, so Aaron has a-11-5 grapes or a-16
Henry got 5 so Henry has h+5
after all this Aaron has 19 fewer grapes than Henry
(a-16) is 19 less than (h+5)
(a-16)+19=(h+5)
a-16+19=h+5
a+3=h+5, and a+h=52
a+h=52, so a=52-h
replace a in a+3=h+5 with 52-h
52-h+3=h+5
55-h=h+5
55=h+h+5
55-5=h+h
50=2h
50/2=h
25=h
Henry has 25 grapes and Aaron has 52-25=27 grapes
check:27-11-5=11, 25+5=30 and 11 is 19 fewer than 30
 
you could also use a+3=h+5 and a+h=52 this way:
a-h=5-3
a-h=2
a+h=52
now add the two equations
2a=54 and a=54/2=27 grapes for Aaron and 25 grapes for Henry