5 beads and 1 marble cost $8.70.
1 bead and 5 marbles cost $17.10.
- Find the cost of 1 bead and 1 marble.
- Find the cost of 1 marble.
- Find the cost of 1 bead.
- Find the cost of 8 beads and 8 marbles.
(a)
5 beads + 1 marble = 8.70 --- (1)
1 bead + 5 marbles = 17.10 --- (2)
(1) + (2)
6 beads + 6 marbles = 8.70 + 17.10
6 beads + 6 marbles = 25.80 --- (3)
(3)
÷ 66 beads + 6 marbles = 25.80
1 bead + 1 marble = 25.80 ÷ 6
1 bead + 1 marble = 4.30 --- (4)
(b)
(2) - (4)
(1 bead + 5 marbles) - (1 bead + 1 marble) = 17.10 - 4.30
1 bead - 1 bead + 5 marbles - 1 marble = 12.80
4 marbles = 12.80
1 marble = 12.80 ÷ 4 = 3.20
Cost of 1 marble = $3.20
(c)
Substitute 1 marble = 3.20 into (4).
1 bead + 1 marble = 4.30
1 bead + 3.20 = 4.30
1 bead = 4.30 - 3.20 = 1.10
Cost of 1 bead = $1.10
(d)
(4)
x 8 1 bead + 1 marble = 4.30
8 x (1 bead + 1 marble) = 8 x 4.30
8 beads + 8 marbles = 34.40
Cost of 8 beads and 8 marbles = $34.40
Answer(s): (a) $4.30; (b) $3.20; (c) $1.10; (d) $34.40