2 marbles and 1 bead cost $10.20.
1 marble and 2 beads cost $7.50.
- 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 9 marbles and 9 beads.
(a)
2 marbles + 1 bead = 10.20 --- (1)
1 marble + 2 beads = 7.50 --- (2)
(1) + (2)
3 marbles + 3 beads = 10.20 + 7.50
3 marbles + 3 beads = 17.70 --- (3)
(3)
÷ 3
3 marbles + 3 beads = 17.70
1 marble + 1 bead = 17.70 ÷ 3
1 marble + 1 bead = 5.90 --- (4)
Cost of 1 marble and 1 bead = $5.90
(b)
(2) - (4)
(1 marble + 2 beads) - (1 marble + 1 marble) = 7.50 - 5.90
1 marble - 1 marble + 2 beads - 1 bead = 1.60
1 bead = 1.60
Cost of 1 bead = $1.60
(c)
Substitute 1 bead = 1.60 into (4).
1 marble + 1 bead = 5.90
1 marble + 1.60 = 5.90
1 marble = 5.90 - 1.60 = 4.30
Cost of 1 marble = $4.30
(d)
(4)
x 9 1 marble + 1 bead = 5.90
9 x (1 marble + 1 marble) = 9 x 5.90
9 marbles + 9 beads = 53.10
Cost of 9 marbles and 9 beads = $53.10
Answer(s): (a) $5.90; (b) $1.60; (c) $4.30; (d) $53.10