Question

1. 1 / 1 points a patient started a new diet that requires each meal to have 460 calories, 6 grams of fiber, and 11 g of fat. the following table shows the fiber, fat, and calorie content of one - serving of each of three breakfast foods.

food	fiber (g)	fat (g)	calories
cottage cheese	0	5	120
toast	2	1	100

how many servings of each food should the patient eat to follow this diet? fruit serving(s) cottage cheese serving(s) toast serving(s)

Explanation:

Step1: Set up equations

Let $x$ be the number of servings of fruit, $y$ be the number of servings of cottage - cheese, and $z$ be the number of servings of toast.
Based on fiber content: $2x + 0y+2z = 6$ (Equation 1).
Based on fat content: $0x + 5y+1z = 11$ (Equation 2).
Based on calorie content: $60x + 120y+100z = 460$ (Equation 3).
Simplify Equation 1 to $x + z=3$, so $x = 3 - z$.
Simplify Equation 3 to $6x + 12y+10z = 46$, or $3x + 6y+5z = 23$.

Step2: Substitute $x$ into other equations

Substitute $x = 3 - z$ into $3x + 6y+5z = 23$.
We get $3(3 - z)+6y+5z = 23$.
Expand: $9-3z + 6y+5z = 23$.
Combine like - terms: $6y + 2z=14$, or $3y+z = 7$, so $z = 7 - 3y$.
Substitute $z = 7 - 3y$ into Equation 2: $5y+(7 - 3y)=11$.

Step3: Solve for $y$

Expand the left - hand side of $5y+(7 - 3y)=11$: $5y + 7-3y = 11$.
Combine like - terms: $2y=4$, so $y = 2$.

Step4: Solve for $z$

Substitute $y = 2$ into $z = 7 - 3y$.
$z=7 - 3\times2=1$.

Step5: Solve for $x$

Substitute $z = 1$ into $x = 3 - z$.
$x = 3 - 1=2$.

Answer:

Fruit: 2 servings, Cottage cheese: 2 servings, Toast: 1 serving