Algebra question

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

This question needs to be solved using a system of equations. There are two equations we need to set up here.

Let x= the number of fishing reels sold

Let y= the number of fishing rods sold

The first equation is:

The number of fishing reels sold + The number of fishing rods sold = Total Cost

2x + 4y = 184

The second equation is:

6x + 3y = 489

Now we have our two equations that need to be solved.

2x + 4y = 184

6x + 3y = 489

There are several ways to solve systems of equations, but let's focus on the elimination method. We must eliminate one of the variables by making the coefficients equal and opposite in the equations.

If we multiply our first equation by -3, it will give us -6x to cancel out the 6x in the second equation

-3(2x + 4y = 184)

-6x - 12y = -552

-6x - 12y = -552

6x + 3y = 489

-9y = -63

y = -63/ -9

y= 7

Then you plug y=7 back into the original equation:

2x + 4y = 184

2x + 4(7) =184

2x + 28 = 184

2x = 184 - 28

2x = 156

x = 156/2

x = 78

So, the price of a reel is $78 and the price of a rod is $7.