This week we learned about solving problems using a grid.
Here is an example using this method:
The first step I did to solve this problem is that I made a grid including all of the information in the problem. The three columns represent the amount, rate and value of each type of coffee/blend mentioned in the problem. In the amount boxes for the Kenyan and Colombian coffee, I put two variable (x for Kenyan and y for Colombian) because the goal is to find out the amount of Colombian coffee in the mix. In the value columns for both coffee I put 5.60x and 3.50y because in the problem it states that the Kenyan coffee costs 5.60 dollars per pound and the Colombian costs 3.50 per pound and it would make sense that the price per pound would be multiplied by how many pounds you need.
The next thing I did was rewrite the information in the grid into equations that can be solved using substitution or elimination.The first equation would be x+y=3 (the amount of Kenyan coffee plus the amount of Colombian equals the amount in the mix). The second equation would be 5.60x+3.50y=11.55 (the amount of Kenyan coffee times it’s price per pound would equal the exact price of Kenyan coffee in the mix. Doing the same to the Colombian coffee and adding it to the exact price of the Kenyan coffee should equal to the price of the mix).
I then solved the question using substitution. In the photo I moved the x to the other side of the equal sign so that y=-x+3. Then I replaced the y in the second equation (5.60x+3.50y=11.55) with -x+3 so that it became 5.60x+3.50(-x+3)=11.55. I then used the law of distribution and simplified the equation to 2.1x+10.5=11.55 then moved the 10.5 to the other side of the equal sign and divided both sides by 2.1. Therefore, the amount of Kenyan coffee in the mix is 0.5 pounds.
To find out the amount of Colombian coffee in the mix I took my first equation (x+y=3) and replaced the x value with 0.5. I then moved it to the other side of the equal sign which left me with y=2.5. To verify if there is really 2.5 pounds of Colombian coffee in the mix I took the same original equation and replaced both variables with their corresponding numbers to see if they would add up to 3. I know that 0.5+2.5=3 which means that my answer is correct and there is indeed 2.5 pounds of Colombian coffee in the mix.