If Adam buys 4 marbles and 5 beads, it costs $50.90.
If Adam buys 5 marbles and 4 beads, he will need another $1.70.
- Find the cost of 1 marble and 1 bead.
- Find the cost of 1 marble.
- Find the cost of 1 bead.
(a)
4 marbles + 5 beads = 50.90 --- (1)
5 marbles + 4 beads = 50.90 + 1.70 = 52.60 --- (2)
(1) + (2)
9 marbles + 9 beads = 103.50 --- (3)
(3)
÷ 9 1 marble + 1 bead = 103.50 ÷ 9 = 11.50 --- (4)
Cost of 1 marble and 1 bead = $11.50
(b)
5 marbles + 4 beads = 52.60 --- (2)
(4)
x 4 4 marbles + 4 beads = 4 x 11.50 = 460 --- (5)
(2) - (5)
5 marbles + 4 beads - 4 marbles - 4 beads = 52.60 - 460
5 marbles - 4 marbles + 4 beads - 4 beads = 6.60
1 marble = 6.60
Cost of 1 marble = $6.60
(c)
Substitute 1 marble = 6.60 into (4).
1 marble + 1 bead = 11.50
6.60 + 1 bead = 11.50
1 bead = 11.50 - 6.60 = 4.90
Cost of 1 bead = $4.90
Answer(s): (a) $11.50; (b) $6.60; (c) $4.90