If Adam buys 5 marbles and 6 beads, it costs $64.20.
If Adam buys 6 marbles and 5 beads, he will have $30 left.
- Find the cost of 1 marble and 1 bead.
- Find the cost of 1 marble.
- Find the cost of 1 bead.
(a)
5 marbles + 6 beads = 64.20 --- (1)
6 marbles + 5 beads = 64.20 - 30 = 61.20 --- (2)
(1) + (2)
11 marbles + 11 beads = 125.40 --- (3)
(3)
÷ 11 1 marble + 1 bead = 125.40 ÷ 11 = 11.40 --- (4)
Cost of 1 marble and 1 bead = $11.40
(b)
(4)
x 5 5 marbles + 5 beads = 5 x 11.40 = 570 --- (5)
(2) - (5)
6 marbles + 5 beads - 5 marbles - 5 beads = 61.20 - 570
6 marbles - 5 marbles - 5 beads + 5 beads = 4.20
1 marble = 4.20
Cost of 1 marble = $4.20
(c)
Substitute 1 marble = 4.20 into (4).
1 marble + 1 bead = 11.40
4.20 + 1 bead = 11.40
1 bead = 11.40 - 4.20 = 7.20
Cost of 1 bead = $7.20
Answer(s): (a) $11.40; (b) $4.20; (c) $7.20