3 marbles and 1 bead cost $10.50.
1 marble and 3 beads cost $9.90.
- 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)
3 marbles + 1 bead = 10.50 --- (1)
1 marble + 3 beads = 9.90 --- (2)
(1) + (2)
4 marbles + 4 beads = 10.50 + 9.90
4 marbles + 4 beads = 20.40 --- (3)
(3)
÷ 44 marbles + 4 beads = 20.40
1 marble + 1 bead = 20.40 ÷ 4
1 marble + 1 bead = 5.10 --- (4)
(b)
(2) - (4)
(1 marble + 3 beads) - (1 marble + 1 marble) = 9.90 - 5.10
1 marble - 1 marble + 3 beads - 1 bead = 4.80
2 beads = 4.80
1 bead = 4.80 ÷ 2 = 2.40
Cost of 1 bead = $2.40
(c)
Substitute 1 bead = 2.40 into (4).
1 marble + 1 bead = 5.10
1 marble + 2.40 = 5.10
1 marble = 5.10 - 2.40 = 2.70
Cost of 1 marble = $2.70
(d)
(4)
x 7 1 marble + 1 bead = 5.10
7 x (1 marble + 1 marble) = 7 x 5.10
7 marbles + 7 beads = 35.70
Cost of 7 marbles and 7 beads = $35.70
Answer(s): (a) $5.10; (b) $2.40; (c) $2.70; (d) $35.70