Question

One serving of soybeans contains 14 grams of protein and 8 grams of fat. One serving of rice contains 4 grams of protein and 1/2 gram of fat. Calculate the number of servings of each that need to be combined, in order to end up with precisely 30 grams of protein and 15 grams of fat. How many servings of rice will be needed?

Answer 1

Answer: 1.8 servings of soybean and 1.2 servings rice will be needed.

Step-by-step explanation:

Let x be the number of soybeans and y be the number of rice.

Then , According to the question , we have

$14x+4y=30\\\Rightarrow\ 7x+2y=15..................................(1)\\\\ 8x+\frac{1}{2}y = 15\\\Rightarrow\ 16x+y=30.............................(2)$

Multiply 2 on both the sides of equation (2), we get

$32x+2y=60................................(3)$

Subtract equation (2) from equation (3), we get

$25x=45\\\\\Rightarrow\ x=1.8$

Put x = 1.8 in equation (2), we get

$16x+y=30\\\\\Rightarrow\ y=30-16x\\=30-16(1.8)=1.2$

Hence, 1.8 servings of soybean and 1.2 servings rice will be needed.