Question 947942

a ratio of 9 to 4. There are 91 string and wind instruments in the orchestra.

let {{{string_instruments=x}}} and {{{wind_instruments=y}}}

{{{x/y=9/4}}}

{{{4x=9y}}}

{{{x =(9/4)y}}}...eq.1

if there are {{{91}}} string and wind instruments in the orchestra, we have

{{{x+y=91}}}.......eq.2

solve the system

{{{x = (9/4)y}}}...eq.1........substitute in eq.2
{{{x+y=91}}}.......eq.2
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{{{(9/4)y+y=91}}}.......eq.2.................solve for {{{y}}}

{{{9y/4+4y/4=91}}}

{{{13y/4=91}}}

{{{13y=91*4}}}

{{{13y=364}}}

{{{y=364/13}}}

{{{y=28}}}

now go to {{{x = (9/4)y}}}...eq.1........substitute {{{28}}} for {{{y}}} and solve for {{{x}}}

{{{x = (9/cross(4))cross(28)7}}}

{{{x = 9*7}}}

{{{x = 63}}}

so, there is:

 {{{highlight( 63)}}} string and  {{{highlight( 28)}}} wind instruments