Respuesta :
Using a system of equations, the amounts of cholesterol in each item are given as follows:
- Egg: 278 mg.
- Cupcake: 14 mg.
- Slice of pizza: 11 mg.
What is a system of equations?
A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
The variables for this problem are given as follows:
- Variable x: Amount of cholesterol in an egg.
- Variable y: Amount of cholesterol in a cupcake.
- Variable z: Amount of cholesterol in a slice of pizza.
By eating 1 egg, 1 cupcake, and 1 slice of pizza, a child consumes 303 mg of cholesterol, hence:
x + y + z = 303.
3 cupcakes and 4 slices of pizza, he or she takes in 90 mg of cholesterol, hence:
3y + 4z = 90
y + 1.33z = 30.
By eating 2 eggs and 1 cupcake, a child consumes 570 mg of cholesterol, hence:
2x + y = 570.
Then, writing y and z as functions of x:
- y = 570 - 2x.
- z = (30 - y)/1.33 = (30 - 570 + 2x)/1.33 = 1.5x - 406.
Then, replacing on the first equation:
x + y + z = 303.
x + 570 - 2x + 1.5x - 406 = 303.
0.5x + 164 = 303.
x = (303 - 164)/0.5
x = 278.
The amounts for the cupcake and the slice of pizza are given as follows:
- y = 570 - 2(278) = 14 mg.
- z = 1.5x - 406 = 1.5(278) - 406 = 11 mg.
More can be learned about a system of equations at https://brainly.com/question/24342899
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