If Adam buys 3 marbles and 4 beads, it costs $40.70.
If Adam buys 4 marbles and 3 beads, he will need another $1.20.
- 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 = 40.70 --- (1)
4 marbles + 3 beads = 40.70 + 1.20 = 41.90 --- (2)
(1) + (2)
7 marbles + 7 beads = 82.60 --- (3)
(3)
÷ 7 1 marble + 1 bead = 82.60 ÷ 7 = 11.80 --- (4)
Cost of 1 marble and 1 bead = $11.80
(b)
4 marbles + 3 beads = 41.90 --- (2)
(4)
x 3 3 marbles + 3 beads = 3 x 11.80 = 35.40 --- (5)
(2) - (5)
4 marbles + 3 beads - 3 marbles - 3 beads = 41.90 - 35.40
4 marbles - 3 marbles + 3 beads - 3 beads = 6.50
1 marble = 6.50
Cost of 1 marble = $6.50
(c)
Substitute 1 marble = 6.50 into (4).
1 marble + 1 bead = 11.80
6.50 + 1 bead = 11.80
1 bead = 11.80 - 6.50 = 5.30
Cost of 1 bead = $5.30
Answer(s): (a) $11.80; (b) $6.50; (c) $5.30