If Adam buys 2 beads and 3 marbles, it costs $29.70.
If Adam buys 3 beads and 2 marbles, he will need another $3.10.
- Find the cost of 1 bead and 1 marble.
- Find the cost of 1 bead.
- Find the cost of 1 marble.
(a)
2 beads + 3 marbles = 29.70 --- (1)
3 beads + 2 marbles = 29.70 + 3.10 = 32.80 --- (2)
(1) + (2)
5 beads + 5 marbles = 62.50 --- (3)
(3)
÷ 5 1 bead + 1 marble = 62.50 ÷ 5 = 12.50 --- (4)
Cost of 1 bead and 1 marble = $12.50
(b)
3 beads + 2 marbles = 32.80 --- (2)
(4)
x 2 2 beads + 2 marbles = 2 x 12.50 = 250 --- (5)
(2) - (5)
3 beads + 2 marbles - 2 beads - 2 marbles = 32.80 - 250
3 beads - 2 beads + 2 marbles - 2 marbles = 7.80
1 bead = 7.80
Cost of 1 bead = $7.80
(c)
Substitute 1 bead = 7.80 into (4).
1 bead + 1 marble = 12.50
7.80 + 1 marble = 12.50
1 marble = 12.50 - 7.80 = 4.70
Cost of 1 marble = $4.70
Answer(s): (a) $12.50; (b) $7.80; (c) $4.70