2 beads and 1 marble cost $11.70.
1 bead and 2 marbles cost $11.10.
- 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 = 11.10 --- (2)
(1) + (2)
3 beads + 3 marbles = 11.70 + 11.10
3 beads + 3 marbles = 22.80 --- (3)
(3)
÷ 3
3 beads + 3 marbles = 22.80
1 bead + 1 marble = 22.80 ÷ 3
1 bead + 1 marble = 7.60 --- (4)
Cost of 1 bead and 1 marble = $7.60
(b)
(2) - (4)
(1 bead + 2 marbles) - (1 bead + 1 marble) = 11.10 - 7.60
1 bead - 1 bead + 2 marbles - 1 marble = 3.50
1 marble = 3.50
Cost of 1 marble = $3.50
(c)
Substitute 1 marble = 3.50 into (4).
1 bead + 1 marble = 7.60
1 bead + 3.50 = 7.60
1 bead = 7.60 - 3.50 = 4.10
Cost of 1 bead = $4.10
(d)
(4)
x 8 1 bead + 1 marble = 7.60
8 x (1 bead + 1 marble) = 8 x 7.60
8 beads + 8 marbles = 60.80
Cost of 8 beads and 8 marbles = $60.80
Answer(s): (a) $7.60; (b) $3.50; (c) $4.10; (d) $60.80