Question

HELP an orchestra consists of string instruments and wind instruments in 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?
Use a system of equations to model each situation.

Answer 1

hmm i see that last answerer wasn't able to help huh

Answer 2

mhm, i need to write equations.

Answer 3

actually that last one was pretty close...did you notice that if you increase the total, you're just multiplying the ratio by a number?

for example, the total is 13

9*1 + 4*1 = 13

if the total is 26

9*2 + 4*2 = 26

if the total is 39

9*3 + 4*3 = 39

do you see this?

Answer 4

yeah.

Answer 5

multiplying by 7 will give 91.

Answer 6

good. so if the total si given to be 91...but the "multiplier" is not given, what do you do?

Answer 7

imagine you don't know it's 7...you have to write equations remember?

Answer 8

what do you do in algebra if there is a number you don't know?

Answer 9

variable.

Answer 10

right. so you multiply 9 and 4 by variables

Answer 11

91=9/4x ?

Answer 12

let's say the variable is x

you get 9x + 4x = 91

Answer 13

no..not 9/4 x

Answer 14

okay. to solve for x we need the other equation

Answer 15

notice what i was doing a while ago

9*1 + 4*1 = 13
9*2 + 4*2 = 26
9*3 + 4*3 = 39

so if you don't know the multiplier...
9*x + 4*x = 39

Answer 16

no wait.

Answer 17

that's 91 not 39

Answer 18

what other equation?

Answer 19

"system of equations"

Answer 20

i know you can combine 9x and 4x into 13x which will give 7 for x.

Answer 21

right

Answer 22

no need for system of equations

Answer 23

you just have 9x + 4x = 91 <--one equation

Answer 24

the rest are just substitutions

Answer 25

i don't know if you call that a system...but it's substitution

Answer 26

to get the number of wind, do 9x

to get the number of string, do 4x

Answer 27

or maybe...this is what you mean

w = 9x
s = 4x

w + s = 91
9x + 4x = 91

Answer 28

i have to leave now...so i hope you get your answer...

Answer 29

63 string, 28 wind.

Answer 30

w+s=91
w=9x
s=4x
------
9x+4x=91
9(7)+4(7)=91
63+28=91
91=91

Answer 31

yeah i got it. thank you :D