If Adam buys 2 marbles and 3 beads, it costs $32.20.
If Adam buys 3 marbles and 2 beads, he will need another $3.10.
- Find the cost of 1 marble and 1 bead.
- Find the cost of 1 marble.
- Find the cost of 1 bead.
(a)
2 marbles + 3 beads = 32.20 --- (1)
3 marbles + 2 beads = 32.20 + 3.10 = 35.30 --- (2)
(1) + (2)
5 marbles + 5 beads = 67.50 --- (3)
(3)
÷ 5 1 marble + 1 bead = 67.50 ÷ 5 = 13.50 --- (4)
Cost of 1 marble and 1 bead = $13.50
(b)
3 marbles + 2 beads = 35.30 --- (2)
(4)
x 2 2 marbles + 2 beads = 2 x 13.50 = 270 --- (5)
(2) - (5)
3 marbles + 2 beads - 2 marbles - 2 beads = 35.30 - 270
3 marbles - 2 marbles + 2 beads - 2 beads = 8.30
1 marble = 8.30
Cost of 1 marble = $8.30
(c)
Substitute 1 marble = 8.30 into (4).
1 marble + 1 bead = 13.50
8.30 + 1 bead = 13.50
1 bead = 13.50 - 8.30 = 5.20
Cost of 1 bead = $5.20
Answer(s): (a) $13.50; (b) $8.30; (c) $5.20