2 marbles and 1 bead cost $7.30.
1 marble and 2 beads cost $9.80.
- 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 = 7.30 --- (1)
1 marble + 2 beads = 9.80 --- (2)
(1) + (2)
3 marbles + 3 beads = 7.30 + 9.80
3 marbles + 3 beads = 17.10 --- (3)
(3)
÷ 3
3 marbles + 3 beads = 17.10
1 marble + 1 bead = 17.10 ÷ 3
1 marble + 1 bead = 5.70 --- (4)
Cost of 1 marble and 1 bead = $5.70
(b)
(2) - (4)
(1 marble + 2 beads) - (1 marble + 1 marble) = 9.80 - 5.70
1 marble - 1 marble + 2 beads - 1 bead = 4.10
1 bead = 4.10
Cost of 1 bead = $4.10
(c)
Substitute 1 bead = 4.10 into (4).
1 marble + 1 bead = 5.70
1 marble + 4.10 = 5.70
1 marble = 5.70 - 4.10 = 1.60
Cost of 1 marble = $1.60
(d)
(4)
x 6 1 marble + 1 bead = 5.70
6 x (1 marble + 1 marble) = 6 x 5.70
6 marbles + 6 beads = 34.20
Cost of 6 marbles and 6 beads = $34.20
Answer(s): (a) $5.70; (b) $4.10; (c) $1.60; (d) $34.20