If Adam buys 3 marbles and 4 beads, it costs $39.40.
If Adam buys 4 marbles and 3 beads, he will need another $3.10.
- 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 = 39.40 --- (1)
4 marbles + 3 beads = 39.40 + 3.10 = 42.50 --- (2)
(1) + (2)
7 marbles + 7 beads = 81.90 --- (3)
(3)
÷ 7 1 marble + 1 bead = 81.90 ÷ 7 = 11.70 --- (4)
Cost of 1 marble and 1 bead = $11.70
(b)
4 marbles + 3 beads = 42.50 --- (2)
(4)
x 3 3 marbles + 3 beads = 3 x 11.70 = 35.10 --- (5)
(2) - (5)
4 marbles + 3 beads - 3 marbles - 3 beads = 42.50 - 35.10
4 marbles - 3 marbles + 3 beads - 3 beads = 7.40
1 marble = 7.40
Cost of 1 marble = $7.40
(c)
Substitute 1 marble = 7.40 into (4).
1 marble + 1 bead = 11.70
7.40 + 1 bead = 11.70
1 bead = 11.70 - 7.40 = 4.30
Cost of 1 bead = $4.30
Answer(s): (a) $11.70; (b) $7.40; (c) $4.30