If Adam buys 3 marbles and 4 beads, it costs $43.50.
If Adam buys 4 marbles and 3 beads, he will need another $2.60.
- 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 = 43.50 --- (1)
4 marbles + 3 beads = 43.50 + 2.60 = 46.10 --- (2)
(1) + (2)
7 marbles + 7 beads = 89.60 --- (3)
(3)
÷ 7 1 marble + 1 bead = 89.60 ÷ 7 = 12.80 --- (4)
Cost of 1 marble and 1 bead = $12.80
(b)
4 marbles + 3 beads = 46.10 --- (2)
(4)
x 3 3 marbles + 3 beads = 3 x 12.80 = 38.40 --- (5)
(2) - (5)
4 marbles + 3 beads - 3 marbles - 3 beads = 46.10 - 38.40
4 marbles - 3 marbles + 3 beads - 3 beads = 7.70
1 marble = 7.70
Cost of 1 marble = $7.70
(c)
Substitute 1 marble = 7.70 into (4).
1 marble + 1 bead = 12.80
7.70 + 1 bead = 12.80
1 bead = 12.80 - 7.70 = 5.10
Cost of 1 bead = $5.10
Answer(s): (a) $12.80; (b) $7.70; (c) $5.10