Question

Sue wants to plan a meal with 71 grams of fat and 1755 calories. If hot dogs have 13 grams of fat and 145 calories each and if baked beans have 8 grams of fat and 330 calories per half-cup serving, how many hot dogs and servings of beans should she use?

Answer 1

To determine the number of hot dogs and servings of baked beans that Sue should use to reach her target of 71 grams of fat and 1755 calories, we create a system of equations based on the fat and calorie content of each food item and solve it using algebraic methods, such as substitution or elimination.

Step-by-step explanation:

Sue is looking to plan a meal with 71 grams of fat and 1755 calories. Each hot dog contains 13 grams of fat and 145 calories, and each half-cup serving of baked beans has 8 grams of fat and 330 calories. To solve for the number of hot dogs (let's call it x) and servings of beans (let's call it y), we can set up a system of linear equations:

• 13x + 8y = 71 (The fat equation)
• 145x + 330y = 1755 (The calorie equation)

Solving this system, we find that there are multiple combinations of hot dogs and servings of beans that Sue can use to reach her target of 71 grams of fat and 1755 calories. One potential solution is to use a method like substitution or elimination to identify valid (x, y) pairs that satisfy both equations.

Answer 2

Sue must use 3 hotdogs and 4 half-cup serving of baked beans.

Step-by-step explanation:

Let the number of hot dogs be represented by h

Let the number of baked beans be represented by b

Hot dogs have 13 grams of fat and 145 calories each

Baked beans have 8 grams of fat and 330 calories per half cup serving

Sue wants to plan a meal with 71 grams of fat and 1755 calories.

Grams of Fat from Hotdog + grams of fat from baked beans=71

13h+8b=71....(I)

Similarly,

Calories from hot dog + Calories from baked beans=1755

145h+330b=1755....(II)

We then solve Equations (I) and (II) simultaneously.

13h+8b=71....(I)

145h+330b=1755....(II)

Multiply equation 1 by 145 and equation 2 by 13

1885h+1160b=10295

1885h+4290b=22815

Subtracting

-3130b=-12520

b=4

Substitute b=4 into (I)

13h+(8X4)=71

13h=71-32

13h=39

h=3

Sue must use 3 hotdogs and 4 half-cup serving of baked beans.