SOLUTION: The ratio of Julia’s peas to Vlada’s peas was 3:2. After Julia gave 15 peas to Vlada, she still had 10 more peas than Vlada. How many peas did Julia have to start with?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The ratio of Julia’s peas to Vlada’s peas was 3:2. After Julia gave 15 peas to Vlada, she still had 10 more peas than Vlada. How many peas did Julia have to start with?       Log On


   

Question 1066751: The ratio of Julia’s peas to Vlada’s peas was 3:2. After Julia gave 15 peas to Vlada, she still had 10 more peas than Vlada. How many peas did Julia have to start with?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of Julia's peas to start with
Let +b+ = number of Vlada's peas to start with
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(1) +a%2Fb+=+3%2F2+
(2) +a+-+15+=+b+%2B+15++%2B+10+
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(2) +a+-+15+=+b+%2B+25+
(2) +a+-+b+=+35+
and
(1) +2a+=+3b+
(1) +b+=+%282%2F3%29%2Aa+
Substitute (1) into (2)
-----------------------
(2) +a+-+%282%2F3%29%2Aa+=+35+
(2) +3a+-+2a+=+105+
(2) +a+=+105+
and
(1) +b+=+%282%2F3%29%2Aa+
(1) +b+=+%282%2F3%29%2A105+
(1) +b+=+70+
-----------------------
Julia had 105 peas to start with
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check:
(2) +a+-+b+=+35+
(2) +105+-+70+=+35+
(2) +35+=+35+
OK