SOLUTION: Use a system of equations to model the situation and then solve by any method. An orchestra consists of string instruments and wind instruments in a ratio of 9 to 4. There

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons  -> Linear Equations Lesson -> SOLUTION: Use a system of equations to model the situation and then solve by any method. An orchestra consists of string instruments and wind instruments in a ratio of 9 to 4. There      Log On


   

Question 947942:
Use a system of equations to model the situation and then solve by any method.

An orchestra consists of string instruments and wind instruments in a ratio of 9 to 4. There are 91 string and wind instruments in the orchestra. How many string instruments are there? How many wind instruments?

63 string instruments 28 wind instruments
65 string instruments 26 wind instruments
60 string instruments 31 wind instruments
72 string instruments 19 wind instruments
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

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%2Fy=9%2F4
4x=9y
x+=%289%2F4%29y...eq.1
if there are 91 string and wind instruments in the orchestra, we have
x%2By=91.......eq.2
solve the system
x+=+%289%2F4%29y...eq.1........substitute in eq.2
x%2By=91.......eq.2
---------------------------------------
%289%2F4%29y%2By=91.......eq.2.................solve for y
9y%2F4%2B4y%2F4=91
13y%2F4=91
13y=91%2A4
13y=364
y=364%2F13
y=28
now go to x+=+%289%2F4%29y...eq.1........substitute 28 for y and solve for x
x+=+%289%2Fcross%284%29%29cross%2828%297
x+=+9%2A7
x+=+63
so, there is:
highlight%28+63%29 string and highlight%28+28%29 wind instruments



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!


Use a system of equations to model the situation and then solve by any method.

An orchestra consists of string instruments and wind instruments in a ratio of 9 to 4. There are 91 string and wind instruments in the orchestra. How many string instruments are there? How many wind instruments?

63 string instruments 28 wind instruments
65 string instruments 26 wind instruments
60 string instruments 31 wind instruments
72 string instruments 19 wind instruments
Ratio of 9:4 means that there are 13 (9 + 4) parts

Since there are a total of 91 instruments, then number of strings = %289%2F13%29+%2A+91

Number of winds: %284%2F13%29+%2A+91, or 91 - %289%2F13%29+%2A+91



OR



Let the multiplicative factor be x

Then we can say that: 9x + 4x = 91

Solve for x

Multiply x by 9 to get number of strings

Multiply x by 4, or subtract number of strings from 91 to get number of winds.