)) Rachel is using ribbon to create girls' hair barrettes. For a craft fair in Springfield, she
made 12 small barrettes and 12 large barrettes, using a total of 156 yards of ribbon. Then,
for another craft fair in Norwood, she made 10 small barrettes and 11 large barrettes, which
used a total of 138 yards. How many yards of ribbon does Rachel use for each?

Step-by-step explanation:

Using s and L to represent the amount of ribbon used for small barrettes and large barrettes, respectively, we have ...

  12s +12L = 156

  10s +11L = 138

Dividing the first equation by 12 gives ...

  s +L = 13

Substituting s = 13-L into the second equation gives ...

  10(13 -L) +11L = 138

  130 +L = 138 . . . . . . . simplify

  L = 8 . . . . . . . . . .  subtract 130

  s = 13 -8 = 5 . . . . find s

Rachel uses 5 yards for a small barrette, and 8 yards for a large barrette.