Question

piano x piano x piano =27
piano x guitar = saxaphone x mircrophone
microphone x saxaphone = 6
saxaphone - piano = piano
guitar x saxaphone x microphone = music note

picture: piano, guitar, saxaphone, microphone, music note
value: ___, ___, ___, ___, ___

Answer 1

To solve the problem, let's define variables for each instrument:

- Let \( p \) represent the value of the piano.
- Let \( g \) represent the value of the guitar.
- Let \( s \) represent the value of the saxophone.
- Let \( m \) represent the value of the microphone.
- Let \( n \) represent the value of the music note.

Now, we can translate the given equations into a system of equations using these variables.

1. From the equation \( \text{piano} \times \text{piano} \times \text{piano} = 27 \), we can write:
\[
p^3 = 27 \implies p = 3
\]

2. From the equation \( \text{piano} \times \text{guitar} = \text{saxophone} \times \text{microphone} \), we can express this as:
\[
p \cdot g = s \cdot m
\]

3. From the equation \( \text{microphone} \times \text{saxophone} = 6 \), we have:
\[
m \cdot s = 6
\]

4. The equation \( \text{saxophone} - \text{piano} = \text{piano} \) can be arranged to find \( s \):
\[
s - p = p \implies s = 2p
\]
Substituting \( p = 3 \):
\[
s = 2 \cdot 3 = 6
\]

5. We substitute \( s = 6 \) into the equation \( m \cdot s = 6 \) to find \( m \):
\[
m \cdot 6 = 6 \implies m = 1
\]

6. Now, we substitute \( p = 3 \) and \( s = 6 \) into the equation \( p \cdot g = s \cdot m \):
\[
3 \cdot g = 6 \cdot 1 \implies 3g = 6 \implies g = 2
\]

7. Finally, we look for the value of the music note from the equation \( \text{guitar} \times \text{saxophone} \times \text{microphone} = \text{music note} \):
\[
n = g \cdot s \cdot m = 2 \cdot 6 \cdot 1 = 12
\]

Now, we can summarize our findings:
- \( p = 3 \) (piano)
- \( g = 2 \) (guitar)
- \( s = 6 \) (saxophone)
- \( m = 1 \) (microphone)
- \( n = 12 \) (music note)

Thus, the final values are:
\[
\text{value: } 3, 2, 6, 1, 12
\]