Algebra problem

Question

A sporting good store sells 2 fishing reels and 4 fishing rods for $184. Later, they sell 6 fishing reels and 3 fishing rods for $489. find the price of each

Answer 1

Hi, Sonya.

Okay, so you have 2 equations and 2 unknowns. Let's let:

X = the price of the fishing reels

Y = the price of the fishing rods

Then you can write 2 equations:

2X + 4Y = 184

6X + 3Y = 489

Now, you can solve the system of equations of obtain your answer.

if we multiply the first equation by 3 we get

3(2X + 4Y = 184) = 6X + 12Y = 552

Now you can subtract the 2nd equation from this equation:

6X + 12Y = 552

-(6X + 3Y = 489)

_______________

Thus, you get 9Y = 63

9Y/9 = 63/9

Y = 7

Now, you can substitute Y = 7 into either of the above equations to solve for X.

6X + 3(7) = 489

6X + 21 = 489

6X = 468

X = 78

Now, substitute these values (X = 78 and Y = 7) into the other equation to check your answer:

2(X) + 4(Y) = 184

2(78) + 4(7) =

156 + 28 = 184

Therefore the answers are correct.

The reels each cost $78

The rods each cost $7