2 beads and 1 marble cost $10.50.
1 bead and 2 marbles cost $7.20.
- 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 9 beads and 9 marbles.
(a)
2 beads + 1 marble = 10.50 --- (1)
1 bead + 2 marbles = 7.20 --- (2)
(1) + (2)
3 beads + 3 marbles = 10.50 + 7.20
3 beads + 3 marbles = 17.70 --- (3)
(3)
÷ 3
3 beads + 3 marbles = 17.70
1 bead + 1 marble = 17.70 ÷ 3
1 bead + 1 marble = 5.90 --- (4)
Cost of 1 bead and 1 marble = $5.90
(b)
(2) - (4)
(1 bead + 2 marbles) - (1 bead + 1 marble) = 7.20 - 5.90
1 bead - 1 bead + 2 marbles - 1 marble = 1.30
1 marble = 1.30
Cost of 1 marble = $1.30
(c)
Substitute 1 marble = 1.30 into (4).
1 bead + 1 marble = 5.90
1 bead + 1.30 = 5.90
1 bead = 5.90 - 1.30 = 4.60
Cost of 1 bead = $4.60
(d)
(4)
x 9 1 bead + 1 marble = 5.90
9 x (1 bead + 1 marble) = 9 x 5.90
9 beads + 9 marbles = 53.10
Cost of 9 beads and 9 marbles = $53.10
Answer(s): (a) $5.90; (b) $1.30; (c) $4.60; (d) $53.10