SOLUTION: The city of Waterville has received a grant for $950,000 to spend on various projects: streets, urban renewal, and parks. The mayor has decided that the same amount should be spent

Algebra ->  Systems-of-equations -> SOLUTION: The city of Waterville has received a grant for $950,000 to spend on various projects: streets, urban renewal, and parks. The mayor has decided that the same amount should be spent      Log On


   

Question 627188: The city of Waterville has received a grant for $950,000 to spend on various projects: streets, urban renewal, and parks. The mayor has decided that the same amount should be spent on streets as is spent on parks, and that the amount spent on urban renewal should equal the total amount spent on streets and parks. How much money will the city spend on each project?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = amount spent on streets
Let +b+ = amount spent on parks
Let +c+ = amount spent on urban renewal
given:
(1) +a+%2B+b+%2B+c+=+950000+
(2) +a+=+b+
(3) +c+=+a+%2B+b+
---------------------
Substitute (3) into (1)
(1) +a+%2B+b+%2B+c+=+950000+
(1) +a+%2B+b+%2B+a+%2B+b+=+950000+
(1) +2a+%2B+2b+=+950000+
Substitute (2) into (1)
(1) +2b+%2B+2b+=+950000+
(1) +4b+=+950000+
(1) +b+=+237500+
and, since
(2) +a+=+b+
(2) +a+=+237500+
and
(3) +c+=+a+%2B+b+
(3) +c+=+2%2A237500+
(3) +c+=+475000+
$237,500 = amount spent on streets
$237,500 = amount spent on parks
$475,000 = amount spent on urban renewal
check answer:
(1) +a+%2B+b+%2B+c+=+950000+
(1) +237500+%2B+237500+%2B+475000+=+950000+
(1) +950000+=+950000+
OK