2 beads and 1 marble cost $5.90.
1 bead and 2 marbles cost $6.40.
- 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 7 beads and 7 marbles.
(a)
2 beads + 1 marble = 5.90 --- (1)
1 bead + 2 marbles = 6.40 --- (2)
(1) + (2)
3 beads + 3 marbles = 5.90 + 6.40
3 beads + 3 marbles = 12.30 --- (3)
(3)
÷ 3
3 beads + 3 marbles = 12.30
1 bead + 1 marble = 12.30 ÷ 3
1 bead + 1 marble = 4.10 --- (4)
Cost of 1 bead and 1 marble = $4.10
(b)
(2) - (4)
(1 bead + 2 marbles) - (1 bead + 1 marble) = 6.40 - 4.10
1 bead - 1 bead + 2 marbles - 1 marble = 2.30
1 marble = 2.30
Cost of 1 marble = $2.30
(c)
Substitute 1 marble = 2.30 into (4).
1 bead + 1 marble = 4.10
1 bead + 2.30 = 4.10
1 bead = 4.10 - 2.30 = 1.80
Cost of 1 bead = $1.80
(d)
(4)
x 7 1 bead + 1 marble = 4.10
7 x (1 bead + 1 marble) = 7 x 4.10
7 beads + 7 marbles = 28.70
Cost of 7 beads and 7 marbles = $28.70
Answer(s): (a) $4.10; (b) $2.30; (c) $1.80; (d) $28.70