SOLUTION: Lee spent $1200 on holiday. If he had spent $50 less per day, he would have been able to stay an extra two days. How long was his holiday?

Algebra ->  Equations -> SOLUTION: Lee spent $1200 on holiday. If he had spent $50 less per day, he would have been able to stay an extra two days. How long was his holiday?       Log On


   



Question 1086340: Lee spent $1200 on holiday. If he had spent $50 less per day, he would have been able to stay an extra two days. How long was his holiday?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I think this problem is assuming Lee
spends the same amount each day
Let +d+ = the number of days he actually stays
+1200%2Fd+ = the amount he actully spent each day
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+1200+=+%28+1200%2Fd+-+50+%29%2A%28+d+%2B+2+%29+
+1200+=+1200+-+50d+%2B+2400%2Fd+-+100+
+2400%2Fd+=+50d+%2B+100+
+2400+=+50d%5E2+%2B+100d+
+48+=+d%5E2+%2B+2d+
complete the square
+d%5E2+%2B+2d+%2B+1+=+48+%2B+1+
+%28+d+%2B+1+%29%5E2+=+49+
+d+%2B+1+=+7+
+d+=+6+
+d+=+6+
His holiday was 6 days
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check:
+1200+=+%28+1200%2Fd+-+50+%29%2A%28+d+%2B+2+%29+
+1200+=+%28+1200%2F6+-+50+%29%2A%28+6+%2B+2+%29+
+1200+=+%28+200+-+50+%29%2A8+
+1200+=+150%2A8+
+1200+=+1200+
OK