2 beads and 1 marble cost $10.80.
1 bead and 2 marbles cost $9.30.
- Find the cost of 1 bead and 1 marble.
- Find the cost of 1 marble.
- Find the cost of 1 bead.
- Find the cost of 9 beads and 9 marbles.
(a)
2 beads + 1 marble = 10.80 --- (1)
1 bead + 2 marbles = 9.30 --- (2)
(1) + (2)
3 beads + 3 marbles = 10.80 + 9.30
3 beads + 3 marbles = 20.10 --- (3)
(3)
÷ 3
3 beads + 3 marbles = 20.10
1 bead + 1 marble = 20.10 ÷ 3
1 bead + 1 marble = 6.70 --- (4)
Cost of 1 bead and 1 marble = $6.70
(b)
(2) - (4)
(1 bead + 2 marbles) - (1 bead + 1 marble) = 9.30 - 6.70
1 bead - 1 bead + 2 marbles - 1 marble = 2.60
1 marble = 2.60
Cost of 1 marble = $2.60
(c)
Substitute 1 marble = 2.60 into (4).
1 bead + 1 marble = 6.70
1 bead + 2.60 = 6.70
1 bead = 6.70 - 2.60 = 4.10
Cost of 1 bead = $4.10
(d)
(4)
x 9 1 bead + 1 marble = 6.70
9 x (1 bead + 1 marble) = 9 x 6.70
9 beads + 9 marbles = 60.30
Cost of 9 beads and 9 marbles = $60.30
Answer(s): (a) $6.70; (b) $2.60; (c) $4.10; (d) $60.30