Talia is buying beads to make bracelets. She makes a bracelet with 7 plastic beads and 5 metal beads for $7.25. She makes another bracelet with 9 plastic beads and 3 metal beads for $6.75. Write and solve a system of equations using elimination to find the price of each bead.

Plastic Beads = $0.50Metal Beads = $0.75

p = Plastic Beads

m = Metal Beads

Equations:

7p + 5m = 7.25

9p + 3m = 6.75

Make one pair of coefficients the same:

3 * (7p + 5m = 7.25) = 21p + 15m = 21.75

5 * (9p + 3m = 6.75) = 45p + 15m = 33.75

Remove that coefficient;

(45p + 15m) - (21p + 15m) = 33.75 - 21.75

(45p - 21p) + (15m - 15m) = 33.75 - 21.75

24p = 12

24p / 24 = 12 / 24

p = 0.5

Substitute the result into one of the original equations.

(7 * 0.5) + 5m = 7.25

Rearrange to find the missing value:

7.25 - (7 * 0.5) = 5m

7.25 - 3.5 = 3.75

5m = 3.75

5m / 5 = 3.75 / 5

m = 0.75