Question

Can someone please check my work? Please? I would really appreciate it...
Question~
Solve the following problem using any method of solving systems. CHECK your solutions by substituting your coordinates into BOTH equations and simplifying.
In one week a music store sold 7 violins for a total of $1600. Two different types of violins were sold. One type cost $200 and the other type cost $300. How many of each type of violin did the store sell?

Answer 1

My answer~
4 violins were sold at $300 = $1200
2 were sold at $200 = $400
$1200+$400= $1600

Answer 2

What my teacher said was wrong~
This is not a guess and check problem. REview the real-life example at the end of the lesson and use it as a model for this.

Answer 3

HI!!

Answer 4

it is wrong because 4 violins plus 2 violins is 6 violins and they sold 7

Answer 5

If you would like to see the "real life example" that my teacher is talking about, I will be happy to post that! And hello @misty1212

Answer 6

you want to go ahead and solve it? we need a couple of equations

Answer 7

lol no i really don't
want to solve this one ? (none of these has anything to do with "real life')

Answer 8

I'm not too sure how to...

Answer 9

we need a variable or two variables depending on your teacher

Answer 10

we could say \(x\) is the number of $300 violins and y is the number of $200 violins and then make two equations

Answer 11

since the total number of violins sold is 7, we know \[x+y=7\]

Answer 12

and the total money is $1600 so \[300x+200y=1600\]

Answer 13

oh ok

Answer 14

the first equation is the same as \[y=7-x\] so put it in the second and solve \[300x+200(7-x)=1600\]

Answer 15

ok, could you show me how?

Answer 16

@misty1212

Answer 17

x=2?

Answer 18

300x + 1400x - 200x = 1600
100x = 200
x = 2
Correct.

Now substitute x = 2 in the equation
x + y = 7 and find y.

Answer 19

so 2x+y=7? or y+2x=7?

Answer 20

Neither.
Since x = 2, replace x by 2.
x + y = 7
Rewrite the equation above, substituting 2 for x.
Then solve for y.

Answer 21

2+y=7= 5
y=5?

Answer 22

@mathstudent55 ?

Answer 23

You need to do one step at a time and write always true statements.
The equation we start with is
x + y = 7
We know x = 2, so we replace x with 2:
2 + y = 7
Now we subtract 2 from both sides to isolate y:
2 + y - 2 = 7 - 2
y = 5

You are correct. y = 5, but you cannot write:
2+y=7= 5
because 7 is not equal to 5.

Answer 24

Since we get x = 2 and y = 5, now we see what we had these two variables represent, so we can answer the question.

Answer 25

We look at @misty1212 's statement above:
"we could say x is the number of $300 violins and y is the number of $200 violins and then make two equations "
Since we got x = 2 and y = 5, now we answer:

The store sold 2 $300 violins and 5 $200 violins

Let's check:
2 + 5 = 7, so the number fo violins sold is correct.

2 * $300 + 5 * $200 = $600 + $1000 = $1600
The amount of money also checks, so our solution is correct.

Answer 26

oh ok thank you soo much!! you are a great help!

Answer 27

You're welcome.