If Adam buys 3 marbles and 4 beads, it costs $45.10.
If Adam buys 4 marbles and 3 beads, he will need another $3.60.
- 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 = 45.10 --- (1)
4 marbles + 3 beads = 45.10 + 3.60 = 48.70 --- (2)
(1) + (2)
7 marbles + 7 beads = 93.80 --- (3)
(3)
÷ 7 1 marble + 1 bead = 93.80 ÷ 7 = 13.40 --- (4)
Cost of 1 marble and 1 bead = $13.40
(b)
4 marbles + 3 beads = 48.70 --- (2)
(4)
x 3 3 marbles + 3 beads = 3 x 13.40 = 40.20 --- (5)
(2) - (5)
4 marbles + 3 beads - 3 marbles - 3 beads = 48.70 - 40.20
4 marbles - 3 marbles + 3 beads - 3 beads = 8.50
1 marble = 8.50
Cost of 1 marble = $8.50
(c)
Substitute 1 marble = 8.50 into (4).
1 marble + 1 bead = 13.40
8.50 + 1 bead = 13.40
1 bead = 13.40 - 8.50 = 4.90
Cost of 1 bead = $4.90
Answer(s): (a) $13.40; (b) $8.50; (c) $4.90