If Adam buys 3 marbles and 4 beads, it costs $48.10.
If Adam buys 4 marbles and 3 beads, he will need another $3.20.
- Find the cost of 1 marble and 1 bead.
- Find the cost of 1 marble.
- Find the cost of 1 bead.
(a)
3 marbles + 4 beads = 48.10 --- (1)
4 marbles + 3 beads = 48.10 + 3.20 = 51.30 --- (2)
(1) + (2)
7 marbles + 7 beads = 99.40 --- (3)
(3)
÷ 7 1 marble + 1 bead = 99.40 ÷ 7 = 14.20 --- (4)
Cost of 1 marble and 1 bead = $14.20
(b)
4 marbles + 3 beads = 51.30 --- (2)
(4)
x 3 3 marbles + 3 beads = 3 x 14.20 = 42.60 --- (5)
(2) - (5)
4 marbles + 3 beads - 3 marbles - 3 beads = 51.30 - 42.60
4 marbles - 3 marbles + 3 beads - 3 beads = 8.70
1 marble = 8.70
Cost of 1 marble = $8.70
(c)
Substitute 1 marble = 8.70 into (4).
1 marble + 1 bead = 14.20
8.70 + 1 bead = 14.20
1 bead = 14.20 - 8.70 = 5.50
Cost of 1 bead = $5.50
Answer(s): (a) $14.20; (b) $8.70; (c) $5.50