SOLUTION: three times the number of coconuts is 10 less than twice the number of pineapples. If there are 15 pieces of fruit in all how many are coconuts?

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Question 120507: three times the number of coconuts is 10 less than twice the number of pineapples. If there are 15 pieces of fruit in all how many are coconuts?
Answer by MathLover1(20849) About Me  (Show Source):
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three times the number of coconuts is 10 less than twice the number of pineapples. If there are 15 pieces of fruit in all how many are coconuts?
let the number of coconuts be c, and the number of pineapples be p

given:
c+%2B+p+=+15...............(1)
3c+%2B+10+=+2p..............(2)

solve the system for c to find how many are coconuts

3c+%2B+10+=+2p..............solve for c

3c++=+2p+-+10

c++=+%282p+-+10%29%2F3..............plug c into (1)

%282p+-+10%29%2F3+%2B+p+=+15.........(1)...both sides multiply by 3

3%2A%282p+-+10%29%2F3+%2B+3%2Ap+=+3%2A15

cross%283%29%2A%282p+-+10%29%2Fcross%283%29+%2B+3p+=+45


2p+-+10+%2B+3p++=+45
5p++=+45+%2B+10
5p++=+55+

p++=+55%2F5+
p++=+11+

now find c

c+%2B+p+=+15...............(1).... substitue p
c+%2B+11+=+15
c+=+15+-+11
c+=+4

check if:

3c+%2B+10+=+2p..............(2)...substitue cand p
3%2A4+%2B+10+=+2%2A11
12+%2B+10+=+22
22+=+22