Country A produces about three times the amount of diamonds in carats produced in country B. If the total produced in both countries is 4,000,000 carats, find the amount produced in each country
You could choose suitable variables to represent the output of each country, say A for country A and B for country B. You are given two ways to relate these variables...can you identify the relations and state them mathematically?
Hello marukai47.
Let A be the number of carats produced by A country and B be number of carats produced by B country, since A country produces three times of diamonds than B country, you can let $\displaystyle A=3B$, and you also know that the sum of number of carats produced by both countries is 4,000,000, so you've got second equation, $\displaystyle A+B=4,000,000$. You can solve this system of equations by substituting 3B instead of A in the second equation and you will get $\displaystyle 3B+B=4,000,000$ -> $\displaystyle 4B=4,000,000$ -> $\displaystyle B=\frac{4,000,000}{4}$ -> $\displaystyle B=1,000,000$. Since number of carats produced by B country is 1,000,000 and you know that A country produces 3B carats, you multiply 1,000,000 by 3 and you get that $\displaystyle A=3,000,000$. I hope this helped.