5 beads and 1 marble cost $11.30.
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 7 beads and 7 marbles.
(a)
5 beads + 1 marble = 11.30 --- (1)
1 bead + 5 marbles = 22.90 --- (2)
(1) + (2)
6 beads + 6 marbles = 11.30 + 22.90
6 beads + 6 marbles = 34.20 --- (3)
(3)
÷ 66 beads + 6 marbles = 34.20
1 bead + 1 marble = 34.20 ÷ 6
1 bead + 1 marble = 5.70 --- (4)
(b)
(2) - (4)
(1 bead + 5 marbles) - (1 bead + 1 marble) = 22.90 - 5.70
1 bead - 1 bead + 5 marbles - 1 marble = 17.20
4 marbles = 17.20
1 marble = 17.20 ÷ 4 = 4.30
Cost of 1 marble = $4.30
(c)
Substitute 1 marble = 4.30 into (4).
1 bead + 1 marble = 5.70
1 bead + 4.30 = 5.70
1 bead = 5.70 - 4.30 = 1.40
Cost of 1 bead = $1.40
(d)
(4)
x 7 1 bead + 1 marble = 5.70
7 x (1 bead + 1 marble) = 7 x 5.70
7 beads + 7 marbles = 39.90
Cost of 7 beads and 7 marbles = $39.90
Answer(s): (a) $5.70; (b) $4.30; (c) $1.40; (d) $39.90