2 marbles and 1 bead cost $10.20.
1 marble and 2 beads cost $6.90.
- 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 7 marbles and 7 beads.
(a)
2 marbles + 1 bead = 10.20 --- (1)
1 marble + 2 beads = 6.90 --- (2)
(1) + (2)
3 marbles + 3 beads = 10.20 + 6.90
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) = 6.90 - 5.70
1 marble - 1 marble + 2 beads - 1 bead = 1.20
1 bead = 1.20
Cost of 1 bead = $1.20
(c)
Substitute 1 bead = 1.20 into (4).
1 marble + 1 bead = 5.70
1 marble + 1.20 = 5.70
1 marble = 5.70 - 1.20 = 4.50
Cost of 1 marble = $4.50
(d)
(4)
x 7 1 marble + 1 bead = 5.70
7 x (1 marble + 1 marble) = 7 x 5.70
7 marbles + 7 beads = 39.90
Cost of 7 marbles and 7 beads = $39.90
Answer(s): (a) $5.70; (b) $1.20; (c) $4.50; (d) $39.90