Question

The agricultural department at Texas A&M is planting experimental strains of wheat, rice and soybeans. It costs $2.35 per bushel to buy seed wheat, $5.40 bushel to buy seed rice, and $3.60 per bushel to buy soybean seeds. The department purchased 1700 bushels of seed and paid a total of $4837. The amount of wheat purchased was 3.25 times the combined amount of rice and soybeans purchased. How many bushels of each type of seed did they buy?

Answer 1

Let's let "W" be the number of bushels of seed wheat, "R" be the number of bushels of seed rice, and "S" be the number of bushels of seed soybeans.

We were given there were 1700 bushels of seed purchased in total, and the sum of the number of bushels for each seed would be equal to this total. So, we can formulate our first equation as:

W + R + S = 1700

It was also given the total cost for all the seeds purchased was $4837, and the seeds have different prices: wheat $2.35/bushel, rice $5.40/bushel, and soybeans $3.60/bushel. So, the total cost would be the sum of the product of the number of bushels and the cost per bushel for each seed. This gives us our second equation:

2.35W + 5.40R + 3.60S = 4837

Lastly, it was given the amount of wheat purchased was 3.25 times the combined amount of rice and soybeans purchased. Therefore, we can formulate the equation:

W = 3.25 (R + S)

Substituting the third equation into the first one, we replace "W" with "3.25R + 3.25S", we solve it and find R and S. Substituting "R" and "S" into the third equation, we find "W".

Hence, the department bought 190 bushels of seed rice, 210 bushels of seed soybeans, and 1300 bushels of seed wheat.