Question

Linear Equations CHECK POINT 1 University of Arkansas researchers discovered that we underestimate the number of calories in restaurant meals. The next time you eat out, take the number of calories you think you ate and double it. The researchers concluded. that this number should be a more accurate estimate. The actual number of calories in one portion of hamburger and fries and two portions of fettuccine Alfredo is 4240. The actual number of calories in two portions of hamburger and fries and one portion of fettuccine Alfredo is 3980. Find the actual number of calories in each of these dishes. (Source: Consumer Reports, January/February, 2007) Test Your Calorie I.Q.​

Answer 1

• hamburger and fries: 1240 calories
• fettuccine Alfredo: 1500 calories

Explanation:

You want the number of calories in each dish if 1 portion of hamburger and fries with 2 portions of fettuccine Alfredo has 4240 calories, and 2 portions of hamburger and fries with 1 portion of fettuccine Alfredo has 3980 calories.

Setup

The equations describing the calories in each dish can be written using h and f for the calories in a portion of hamburger and in a portion of fettuccine, respectively:

1h + 2f = 4240

2h +1f = 3980

Solution

Subtracting the first equation from twice the second gives ...

2(2h +f) -(h +2f) = 2(3980) -(4240)

3h = 3710 . . . . . . . simplify

h = 1240 . . . . . . . divide by 3

Then the calories in the fettuccine can be found from the second equation:

f = 3980 -2h = 3980 -2480 = 1500

The actual number of calories in a portion of hamburger and fries is 1240.

The actual number of calories in a portion of fettuccine Alfredo is 1500.

__

Additional comment

The attachment shows a calculator solution using matrix methods.