AN ORCHESTRA CONSISTS OF STRINGS INSTRAMENTS AND WIND INSTIMENTS IN A RATIO OF 9 TO 4. THERE ARE 91 STRINGS AND WIND INSTRUMENTS IN THE ORCHESTRA. hOW MANY STRING INSTRUMENTS ARE THERE? how many wind instruments? Use a system of equation to model each situation. solve by any method.
63 wind and 28 string
7x
To solve this problem, we can set up a system of equations based on the given information.
Let's assume the number of string instruments in the orchestra is "s" and the number of wind instruments is "w".
Based on the given ratio, we can set up the following equation:
s/w = 9/4
We are also told that there are a total of 91 string and wind instruments:
s + w = 91
Now, we can solve this system of equations using any method, such as substitution or elimination.
Substitution Method:
From the first equation, we can express s in terms of w:
s = (9/4)w
Substituting this value of s into the second equation, we get:
(9/4)w + w = 91
(9w + 4w)/4 = 91
13w/4 = 91
13w = 364
w = 28
Now, substitute the value of w back into the first equation to find s:
s = (9/4) * 28
s = 63
Therefore, there are 63 string instruments and 28 wind instruments in the orchestra.
let the number of string instruments be 9x
let the number of wind instruments be 4x
(notice 9x:4x = 9:4)
then 9x + 4x = 91
I will let you finish it.