If Adam buys 5 marbles and 6 beads, it costs $77.10.
If Adam buys 6 marbles and 5 beads, he will have $2.40 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 = 77.10 --- (1)
6 marbles + 5 beads = 77.10 - 2.40 = 74.70 --- (2)
(1) + (2)
11 marbles + 11 beads = 151.80 --- (3)
(3)
÷ 11 1 marble + 1 bead = 151.80 ÷ 11 = 13.80 --- (4)
Cost of 1 marble and 1 bead = $13.80
(b)
(4)
x 5 5 marbles + 5 beads = 5 x 13.80 = 690 --- (5)
(2) - (5)
6 marbles + 5 beads - 5 marbles - 5 beads = 74.70 - 690
6 marbles - 5 marbles - 5 beads + 5 beads = 5.70
1 marble = 5.70
Cost of 1 marble = $5.70
(c)
Substitute 1 marble = 5.70 into (4).
1 marble + 1 bead = 13.80
5.70 + 1 bead = 13.80
1 bead = 13.80 - 5.70 = 8.10
Cost of 1 bead = $8.10
Answer(s): (a) $13.80; (b) $5.70; (c) $8.10