00:01
This problem says a store is selling two mixtures of nuts in 20 ounce bags.
00:04
The first mixture has 15 ounces of peanuts combined with 5 ounces of cashews and costs $4 .75.
00:09
The second mixture has 5 ounces of peanuts and 15 ounces of cashews and costs $6 .25.
00:15
How much does 1 ounce of peanuts and 1 ounce of cashews cost? and to figure this out, we're going to write a system of equations to represent the scenario, and we'll label the cost of 1 ounce of a peanut as x, and then 1 ounce of cashews as y.
00:28
So 15 ounces of peanuts or 15x plus 5 ounces of cashew or 5y equals 475.
00:36
And then we have 5 ounces times x for 5 ounces of peanuts in the second mixture plus 15 ounces of cashews, so 15y, equal to the cost for the second mixture, which is $6 .25.
00:47
And to solve, we'll use elimination where we will multiply our first equation by negative 3, which is going to give us negative 45x minus 15y equal to 3 times the 4 .75, which is going to give us the result of negative 14 .25.
01:09
And now what will happen when we add our second and third equation is that our y values will eliminate because we will have 5x plus negative 45x which gives us negative 40x equal to after the y values eliminate the 6 .25 plus negative 14 .25 which will give us negative 8...