5 beads and 1 marble cost $20.90.
1 bead and 5 marbles cost $22.90.
- 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 = 20.90 --- (1)
1 bead + 5 marbles = 22.90 --- (2)
(1) + (2)
6 beads + 6 marbles = 20.90 + 22.90
6 beads + 6 marbles = 43.80 --- (3)
(3)
÷ 66 beads + 6 marbles = 43.80
1 bead + 1 marble = 43.80 ÷ 6
1 bead + 1 marble = 7.30 --- (4)
(b)
(2) - (4)
(1 bead + 5 marbles) - (1 bead + 1 marble) = 22.90 - 7.30
1 bead - 1 bead + 5 marbles - 1 marble = 15.60
4 marbles = 15.60
1 marble = 15.60 ÷ 4 = 3.90
Cost of 1 marble = $3.90
(c)
Substitute 1 marble = 3.90 into (4).
1 bead + 1 marble = 7.30
1 bead + 3.90 = 7.30
1 bead = 7.30 - 3.90 = 3.40
Cost of 1 bead = $3.40
(d)
(4)
x 8 1 bead + 1 marble = 7.30
8 x (1 bead + 1 marble) = 8 x 7.30
8 beads + 8 marbles = 58.40
Cost of 8 beads and 8 marbles = $58.40
Answer(s): (a) $7.30; (b) $3.90; (c) $3.40; (d) $58.40