one model of stereo sold for $118. another sold for $92. 32 stereos were sold with receipts totaling 3,230. How many of each type were sold?

Question

need a system of equations

Answer 1

the answer here will come from two simultaneous equations

 

let x = the number sold at $118, and y = the number sold at $92

 

1. $118x + $92y = $3230

2.        x +      y =       32

3. solve equation 2 for x = 32 - y

4. substitute the value for x into equation 1

5. equation 1 becomes $118 (32 - y) + $92y = $3230

6. expand equation 1 to $3776 - 118y + $92y = $3230

7. add $118y to both sides, and subtract $3230 from both sides, which yields $546 = 26y; thus 21 = y, and then x = 32 - 21 = 11

the answer is 11 stereos @ $118 each and $21 stereos @ $92 each

Proof: (11 • $118) + (21 • $92) = $1298 + $1932 = $3230