Question

One bar of candy A and two bars of candy B have 774 calories. two bars of candy A and one bar of candy B contain 789 calories find a colored content of each

Answer 1

A: 268 calories

B: 253 calories

Explanation:

You have probably been taught substitution and elimination methods of solving a system of equations. There are other methods as well. Here's one that works for this system. It is based on the symmetry of the system and the fact that the coefficients differ by 1.

We note that each of the equations can be written in terms of A+B:

(A+B) +B = 774

A +(A+B) = 789

We also note that if we add these two equations, we get a sum that is 3(A+B):

3(A+B) = 774 +789 = 1563

A+B = 521 . . . . . . divide by 3

Then ...

B = 774 -(A+B) = 774 -521

B = 253

__

A = 789 -(A+B) = 789 -521

A = 268

One bar of candy A has 268 calories; one bar of candy B has 253 calories.