Question

The top three corn producers in the world​ - country​ A, country​ B, and country C​ - grew a total of about 664 million metric tons​ (MT) of corn in 2014. The country A produced 82 million MT more than the combined production of country B and country C. Country B produced 177 million MT more than country C. Find the number of metric tons of corn produced by each country.  

Answer 1

Answer:

Number of metric tons of corn produced by country A = 373 million MT

Number of metric tons of corn produced by country B = 234 million MT

Number of metric tons of corn produced by country C = 57 million MT

Step-by-step explanation:

From the given information we have

A+B+C = 664 ____equation(1)

A = B+C+82 ____equation(2)

B = C + 177 ____equation(3)

1) Plugging in B=C+177 into equation 2, we get

A = B+C+82

=> A = (C+177) + C +82

=> A = C+177+C+82

=> A = C +C +177+82

=> A= 2C +  259 ____let it be equation (4)

2) Plugging in A=2C+259 from equation 4 and B=C+177 from equation 3 into the equation 1, we get

A+B+C = 664

=> (2C+259)+(C+177)+C = 664

=> 2C+C+C+259+177 = 664

=> 4C + 436 = 664

3) Subtracting 436 from both the sides, we have

4C + 436 - 436 = 664 - 436

4) Cancelling out +436 and -436 from the left side, we get

4C = 228

5) Dividing both the sides by 4, we get

$\frac{4C}{4} = \frac{228}{4}$

6) Cancelling out the 4's from the left, we get

C = 57

7) Plugging in C=57 into the equation 3, we get

B = C + 177

=> B = 57+177

=> B = 234

8) Plugging in B=234 and C=57 into the equation 1, we get

A+B+C = 664

=> A+234+57=664

=> A + 291= 664

9) Subtracting 291 from both the sides, we get

A + 291 - 291 = 664 - 291

10) Cancelling out +291 and -291 from the left side, we get

A = 373

So, A = 373, B= 234, C=57