5 beads and 1 marble cost $9.10.
1 bead and 5 marbles cost $19.10.
- 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 7 beads and 7 marbles.
(a)
5 beads + 1 marble = 9.10 --- (1)
1 bead + 5 marbles = 19.10 --- (2)
(1) + (2)
6 beads + 6 marbles = 9.10 + 19.10
6 beads + 6 marbles = 28.20 --- (3)
(3)
÷ 66 beads + 6 marbles = 28.20
1 bead + 1 marble = 28.20 ÷ 6
1 bead + 1 marble = 4.70 --- (4)
(b)
(2) - (4)
(1 bead + 5 marbles) - (1 bead + 1 marble) = 19.10 - 4.70
1 bead - 1 bead + 5 marbles - 1 marble = 14.40
4 marbles = 14.40
1 marble = 14.40 ÷ 4 = 3.60
Cost of 1 marble = $3.60
(c)
Substitute 1 marble = 3.60 into (4).
1 bead + 1 marble = 4.70
1 bead + 3.60 = 4.70
1 bead = 4.70 - 3.60 = 1.10
Cost of 1 bead = $1.10
(d)
(4)
x 7 1 bead + 1 marble = 4.70
7 x (1 bead + 1 marble) = 7 x 4.70
7 beads + 7 marbles = 32.90
Cost of 7 beads and 7 marbles = $32.90
Answer(s): (a) $4.70; (b) $3.60; (c) $1.10; (d) $32.90