If Adam buys 3 marbles and 4 beads, it costs $51.70.
If Adam buys 4 marbles and 3 beads, he will have $2.60 left.
- 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 = 51.70 --- (1)
4 marbles + 3 beads = 51.70 - 2.60 = 49.10 --- (2)
(1) + (2)
7 marbles + 7 beads = 100.80 --- (3)
(3)
÷ 7 1 marble + 1 bead = 100.80 ÷ 7 = 14.40 --- (4)
Cost of 1 marble and 1 bead = $14.40
(b)
(4)
x 3 3 marbles + 3 beads = 3 x 14.40 = 43.20 --- (5)
(2) - (5)
4 marbles + 3 beads - 3 marbles - 3 beads = 49.10 - 43.20
4 marbles - 3 marbles - 3 beads + 3 beads = 5.90
1 marble = 5.90
Cost of 1 marble = $5.90
(c)
Substitute 1 marble = 5.90 into (4).
1 marble + 1 bead = 14.40
5.90 + 1 bead = 14.40
1 bead = 14.40 - 5.90 = 8.50
Cost of 1 bead = $8.50
Answer(s): (a) $14.40; (b) $5.90; (c) $8.50