2 beads and 1 marble cost $11.50.
1 bead and 2 marbles cost $11.60.
- 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 5 beads and 5 marbles.
(a)
2 beads + 1 marble = 11.50 --- (1)
1 bead + 2 marbles = 11.60 --- (2)
(1) + (2)
3 beads + 3 marbles = 11.50 + 11.60
3 beads + 3 marbles = 23.10 --- (3)
(3)
÷ 3
3 beads + 3 marbles = 23.10
1 bead + 1 marble = 23.10 ÷ 3
1 bead + 1 marble = 7.70 --- (4)
Cost of 1 bead and 1 marble = $7.70
(b)
(2) - (4)
(1 bead + 2 marbles) - (1 bead + 1 marble) = 11.60 - 7.70
1 bead - 1 bead + 2 marbles - 1 marble = 3.90
1 marble = 3.90
Cost of 1 marble = $3.90
(c)
Substitute 1 marble = 3.90 into (4).
1 bead + 1 marble = 7.70
1 bead + 3.90 = 7.70
1 bead = 7.70 - 3.90 = 3.80
Cost of 1 bead = $3.80
(d)
(4)
x 5 1 bead + 1 marble = 7.70
5 x (1 bead + 1 marble) = 5 x 7.70
5 beads + 5 marbles = 38.50
Cost of 5 beads and 5 marbles = $38.50
Answer(s): (a) $7.70; (b) $3.90; (c) $3.80; (d) $38.50