Harmonica = $8
Recorder = $6
We’ll call r the cost of a recorder, h the cost of a harmonica.
5r + 4h = 62
10r + 3h = 84
First, we’ll solve for r in terms of h:
10r = 84 -3h
r = 8.4 - 0.3h
Then we’ll substitute that expression for r in the other equation:
5(8.4 - 0.3h) + 4h = 62
42 - 1.5h + 4h = 62
2.5h = 20
h = 8
Then we’ll substitute that in to solve for the numerical value of r
r = 8.4 - 0.3h
r = 8.4 - 0.3(8)
r = 8.4 - 2.4
r = 6
Check the math:
5r + 4h = 62
5(6) + 4(8) = 30 + 32 = 62
Let me know if you have any questions.