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

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) (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 and

...eq.1
if there are string and wind instruments in the orchestra, we have
.......eq.2
solve the system
...eq.1........substitute in eq.2
.......eq.2
---------------------------------------
.......eq.2.................solve for

now go to ...eq.1........substitute for and solve for

so, there is:
string and wind instruments

Answer by MathTherapy(10552) (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 =
Number of winds: , or 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.
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