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?

let the number of coconuts be {{{c}}}, and the number of pineapples be {{{p}}}


given:

{{{c + p = 15}}}...............(1) 

{{{3c + 10 = 2p}}}..............(2)


solve the system for {{{c}}} to find how many are coconuts


{{{3c + 10 = 2p}}}..............solve for {{{c}}}


{{{3c  = 2p - 10}}}


{{{c  = (2p - 10)/3}}}..............plug {{{c}}} into (1)


{{{(2p - 10)/3 + p = 15}}}.........(1)...both sides multiply by {{{3}}} 


{{{3*(2p - 10)/3 + 3*p = 3*15}}}


{{{cross(3)*(2p - 10)/cross(3) + 3p = 45}}}



{{{2p - 10 + 3p  = 45}}} 

{{{5p  = 45 + 10}}} 

{{{5p  = 55 }}}
 
{{{p  = 55/5 }}} 

{{{p  = 11 }}}


now find {{{c}}}


{{{c + p = 15}}}...............(1).... substitue {{{p}}}

{{{c + 11 = 15}}}

{{{c = 15 - 11}}}

{{{c = 4}}}


check if:


{{{3c + 10 = 2p}}}..............(2)...substitue {{{c}}}and {{{p}}}

{{{3*4 + 10 = 2*11}}}

{{{12 + 10 = 22}}}

{{{22 = 22}}}