2 marbles and 1 bead cost $7.10.
1 marble and 2 beads cost $5.50.
- Find the cost of 1 marble and 1 bead.
- Find the cost of 1 bead.
- Find the cost of 1 marble.
- Find the cost of 6 marbles and 6 beads.
(a)
2 marbles + 1 bead = 7.10 --- (1)
1 marble + 2 beads = 5.50 --- (2)
(1) + (2)
3 marbles + 3 beads = 7.10 + 5.50
3 marbles + 3 beads = 12.60 --- (3)
(3)
÷ 3
3 marbles + 3 beads = 12.60
1 marble + 1 bead = 12.60 ÷ 3
1 marble + 1 bead = 4.20 --- (4)
Cost of 1 marble and 1 bead = $4.20
(b)
(2) - (4)
(1 marble + 2 beads) - (1 marble + 1 marble) = 5.50 - 4.20
1 marble - 1 marble + 2 beads - 1 bead = 1.30
1 bead = 1.30
Cost of 1 bead = $1.30
(c)
Substitute 1 bead = 1.30 into (4).
1 marble + 1 bead = 4.20
1 marble + 1.30 = 4.20
1 marble = 4.20 - 1.30 = 2.90
Cost of 1 marble = $2.90
(d)
(4)
x 6 1 marble + 1 bead = 4.20
6 x (1 marble + 1 marble) = 6 x 4.20
6 marbles + 6 beads = 25.20
Cost of 6 marbles and 6 beads = $25.20
Answer(s): (a) $4.20; (b) $1.30; (c) $2.90; (d) $25.20