If Adam buys 2 marbles and 3 beads, it costs $29.10.
If Adam buys 3 marbles and 2 beads, he will need another $1.30.
- 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 = 29.10 --- (1)
3 marbles + 2 beads = 29.10 + 1.30 = 30.40 --- (2)
(1) + (2)
5 marbles + 5 beads = 59.50 --- (3)
(3)
÷ 5 1 marble + 1 bead = 59.50 ÷ 5 = 11.90 --- (4)
Cost of 1 marble and 1 bead = $11.90
(b)
3 marbles + 2 beads = 30.40 --- (2)
(4)
x 2 2 marbles + 2 beads = 2 x 11.90 = 23.80 --- (5)
(2) - (5)
3 marbles + 2 beads - 2 marbles - 2 beads = 30.40 - 23.80
3 marbles - 2 marbles + 2 beads - 2 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 = 11.90
6.60 + 1 bead = 11.90
1 bead = 11.90 - 6.60 = 5.30
Cost of 1 bead = $5.30
Answer(s): (a) $11.90; (b) $6.60; (c) $5.30