2 marbles and 1 bead cost $4.70.
1 marble and 2 beads cost $5.20.
- 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 = 4.70 --- (1)
1 marble + 2 beads = 5.20 --- (2)
(1) + (2)
3 marbles + 3 beads = 4.70 + 5.20
3 marbles + 3 beads = 9.90 --- (3)
(3)
÷ 3
3 marbles + 3 beads = 9.90
1 marble + 1 bead = 9.90 ÷ 3
1 marble + 1 bead = 3.30 --- (4)
Cost of 1 marble and 1 bead = $3.30
(b)
(2) - (4)
(1 marble + 2 beads) - (1 marble + 1 marble) = 5.20 - 3.30
1 marble - 1 marble + 2 beads - 1 bead = 1.90
1 bead = 1.90
Cost of 1 bead = $1.90
(c)
Substitute 1 bead = 1.90 into (4).
1 marble + 1 bead = 3.30
1 marble + 1.90 = 3.30
1 marble = 3.30 - 1.90 = 1.40
Cost of 1 marble = $1.40
(d)
(4)
x 6 1 marble + 1 bead = 3.30
6 x (1 marble + 1 marble) = 6 x 3.30
6 marbles + 6 beads = 19.80
Cost of 6 marbles and 6 beads = $19.80
Answer(s): (a) $3.30; (b) $1.90; (c) $1.40; (d) $19.80