a. Let c and b represent the numbers of capped and broken bottles, respectively. Here is the system of equations.
... c + b = 15 . . . . 15 bottles have come Erica's way
... 4c -2b = 6 . . . .Erica's net pay for the day is 6 cents
b. By substitution, we can write an expression for b in terms of c:
... b = 15 - c
Then put it into the second equation:
... 4c - 2(15-c) = 6
... 6c - 30 = 6 . . . . eliminate parentheses
... 6c = 36 . . . . . . .add 30
... c = 6 . . . . . . . . . divide by 6
... b = 15 - 6 = 9 . . find the value of b
Erica has capped 6 bottles and broken 9.
_____
Here's one way to do it by elimination. We can divide the second equation by 2 to put it into standard form:
... 2c - b = 3
Now, adding it to the first equation gives
... (2c -b) + (c +b) = (3) + (15)
... 3c = 18 . . . . . simplify. Notice the b variable has been eliminated
... c = 6 . . . . . . . divide by 3
... 6 + b = 15
... b = 9 . . . . . . substitute into the first equation and solve for b by subtracting 6
Erica has capped 6 bottles and broken 9. (same solution as above)
