SOLUTION: 1. one number is 2 more than 5 times the other. their product is 24 find the numbers how would i do this because i dont get it. 2. parts for an automoblie repair cost 175. the m

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: 1. one number is 2 more than 5 times the other. their product is 24 find the numbers how would i do this because i dont get it. 2. parts for an automoblie repair cost 175. the m      Log On

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Question 507623: 1. one number is 2 more than 5 times the other. their product is 24 find the numbers how would i do this because i dont get it.
2. parts for an automoblie repair cost 175. the mechanic charges 34 per hour. if you receive an estimate for at least 226 and at most 294 for fixing the car, what is the time interval that the mechanic will be working on the job? i dont get this one either.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the numbers x and y
given:
(1) +x+=+5y+%2B+2+
(2) +x%2Ay+=+24+
Substitute (1) into (2)
(2) +%285y+%2B+2%29%2Ay+=+24+
(2) +5y%5E2+%2B+2y+-+24+=+0+
Use the quadratic formula
y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+5+
+b+=+2+
+c+=+-24+
y+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A5%2A%28-24%29+%29%29%2F%282%2A5%29+
y+=+%28-2+%2B-+sqrt%28+4+%2B+480+%29%29%2F+10+
y+=+%28-2+%2B-+sqrt%28+484+%29%29%2F+10+
+y+=+%28-2+%2B+22%29+%2F+10+
+y+=+2+
and, since
+x+=+5y+%2B+2+
+x+=+5%2A2+%2B+2+
+x+=+12+
The numbers are 12 and 2
(2)
Subtract the cost of parts from max and min
+226+-+175+=+51+
+294+-+175+=+119+
The mechanic works at least +51%2F34+=+1.5+ hrs
and, at the most, +119%2F34+=+3.5+ hrs
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Note that ( dollars ) / ( dollars per hr ) = hours