2 marbles and 1 bead cost $10.40.
1 marble and 2 beads cost $10.30.
- 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 = 10.40 --- (1)
1 marble + 2 beads = 10.30 --- (2)
(1) + (2)
3 marbles + 3 beads = 10.40 + 10.30
3 marbles + 3 beads = 20.70 --- (3)
(3)
÷ 3
3 marbles + 3 beads = 20.70
1 marble + 1 bead = 20.70 ÷ 3
1 marble + 1 bead = 6.90 --- (4)
Cost of 1 marble and 1 bead = $6.90
(b)
(2) - (4)
(1 marble + 2 beads) - (1 marble + 1 marble) = 10.30 - 6.90
1 marble - 1 marble + 2 beads - 1 bead = 3.40
1 bead = 3.40
Cost of 1 bead = $3.40
(c)
Substitute 1 bead = 3.40 into (4).
1 marble + 1 bead = 6.90
1 marble + 3.40 = 6.90
1 marble = 6.90 - 3.40 = 3.50
Cost of 1 marble = $3.50
(d)
(4)
x 6 1 marble + 1 bead = 6.90
6 x (1 marble + 1 marble) = 6 x 6.90
6 marbles + 6 beads = 41.40
Cost of 6 marbles and 6 beads = $41.40
Answer(s): (a) $6.90; (b) $3.40; (c) $3.50; (d) $41.40