2 beads and 1 marble cost $11.70.
1 bead and 2 marbles cost $10.20.
- 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 8 beads and 8 marbles.
(a)
2 beads + 1 marble = 11.70 --- (1)
1 bead + 2 marbles = 10.20 --- (2)
(1) + (2)
3 beads + 3 marbles = 11.70 + 10.20
3 beads + 3 marbles = 21.90 --- (3)
(3)
÷ 3
3 beads + 3 marbles = 21.90
1 bead + 1 marble = 21.90 ÷ 3
1 bead + 1 marble = 7.30 --- (4)
Cost of 1 bead and 1 marble = $7.30
(b)
(2) - (4)
(1 bead + 2 marbles) - (1 bead + 1 marble) = 10.20 - 7.30
1 bead - 1 bead + 2 marbles - 1 marble = 2.90
1 marble = 2.90
Cost of 1 marble = $2.90
(c)
Substitute 1 marble = 2.90 into (4).
1 bead + 1 marble = 7.30
1 bead + 2.90 = 7.30
1 bead = 7.30 - 2.90 = 4.40
Cost of 1 bead = $4.40
(d)
(4)
x 8 1 bead + 1 marble = 7.30
8 x (1 bead + 1 marble) = 8 x 7.30
8 beads + 8 marbles = 58.40
Cost of 8 beads and 8 marbles = $58.40
Answer(s): (a) $7.30; (b) $2.90; (c) $4.40; (d) $58.40