Jim wants to plan a meal with 134 grams of carbohydrates and

Jim wants to plan a meal with 134 grams of carbohydrates and 1180 calories. If green beans have 7 grams of carbohydrates and 30 calories per half-cup serving and french shrimp have 9 grams of carbohydrates and 190 calories per three-ounce serving, how many servings of green beans and shrimp should he use?

Solution

Let:
x= number of half-cup servings of beans
y= number of 3 oz. servings of shrimp

We will have 2 equarions, one for carbs and one for calories

7x+9y=74
30x+190y=620

30(7x + 9y) = 30(74)
-7(30x + 190y) = -7(620)

210x + 270y = 2220
-210x - 1330y = -4340

-1060y = -2120

y = 2

7x + 9y = 74
7x + 9(2) = 74
7x + 18 = 74
7x = 56
x = 8