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# word problem

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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
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#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
#2
+1

Thank you!

Guest Nov 15, 2017

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