4 beads and 1 marble cost $11.90.
1 bead and 4 marbles cost $8.60.
- 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)
4 beads + 1 marble = 11.90 --- (1)
1 bead + 4 marbles = 8.60 --- (2)
(1) + (2)
5 beads + 5 marbles = 11.90 + 8.60
5 beads + 5 marbles = 20.50 --- (3)
(3)
÷ 55 beads + 5 marbles = 20.50
1 bead + 1 marble = 20.50 ÷ 5
1 bead + 1 marble = 4.10 --- (4)
(b)
(2) - (4)
(1 bead + 4 marbles) - (1 bead + 1 marble) = 8.60 - 4.10
1 bead - 1 bead + 4 marbles - 1 marble = 4.50
3 marbles = 4.50
1 marble = 4.50 ÷ 3 = 1.50
Cost of 1 marble = $1.50
(c)
Substitute 1 marble = 1.50 into (4).
1 bead + 1 marble = 4.10
1 bead + 1.50 = 4.10
1 bead = 4.10 - 1.50 = 2.60
Cost of 1 bead = $2.60
(d)
(4)
x 5 1 bead + 1 marble = 4.10
5 x (1 bead + 1 marble) = 5 x 4.10
5 beads + 5 marbles = 20.50
Cost of 5 beads and 5 marbles = $20.50
Answer(s): (a) $4.10; (b) $1.50; (c) $2.60; (d) $20.50