A sporting goods store sells 3 fishing reels and 5 fishing rods for $488. Later they sell 6 fishing reels and 6 fishing rods for $588. FInd the price of each item.
Fishing reel =r
Fishing Rod=R
3r + 5R =488,
6r + 6R =588, solve for r, R
Solve the following system:
{3 r + 5 R = 488 | (equation 1)
6 r + 6 R = 588 | (equation 2)
Swap equation 1 with equation 2:
{6 r + 6 R = 588 | (equation 1)
3 r + 5 R = 488 | (equation 2)
Subtract 1/2 × (equation 1) from equation 2:
{6 r + 6 R = 588 | (equation 1)
0 r+2 R = 194 | (equation 2)
Divide equation 1 by 6:
{r + R = 98 | (equation 1)
0 r+2 R = 194 | (equation 2)
Divide equation 2 by 2:
{r + R = 98 | (equation 1)
0 r+R = 97 | (equation 2)
Subtract equation 2 from equation 1:
{r+0 R = 1 | (equation 1)
0 r+R = 97 | (equation 2)
Collect results:
r = $1.00 and R=$97.00
