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.

Guest Nov 15, 2017

#1**+1 **

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**

Guest Nov 15, 2017