5 marbles and 1 bead cost $20.30.
1 marble and 5 beads cost $19.90.
- Find the cost of 1 marble and 1 bead.
- Find the cost of 1 bead.
- Find the cost of 1 marble.
- Find the cost of 7 marbles and 7 beads.
(a)
5 marbles + 1 bead = 20.30 --- (1)
1 marble + 5 beads = 19.90 --- (2)
(1) + (2)
6 marbles + 6 beads = 20.30 + 19.90
6 marbles + 6 beads = 40.20 --- (3)
(3)
÷ 66 marbles + 6 beads = 40.20
1 marble + 1 bead = 40.20 ÷ 6
1 marble + 1 bead = 6.70 --- (4)
(b)
(2) - (4)
(1 marble + 5 beads) - (1 marble + 1 marble) = 19.90 - 6.70
1 marble - 1 marble + 5 beads - 1 bead = 13.20
4 beads = 13.20
1 bead = 13.20 ÷ 4 = 3.30
Cost of 1 bead = $3.30
(c)
Substitute 1 bead = 3.30 into (4).
1 marble + 1 bead = 6.70
1 marble + 3.30 = 6.70
1 marble = 6.70 - 3.30 = 3.40
Cost of 1 marble = $3.40
(d)
(4)
x 7 1 marble + 1 bead = 6.70
7 x (1 marble + 1 marble) = 7 x 6.70
7 marbles + 7 beads = 46.90
Cost of 7 marbles and 7 beads = $46.90
Answer(s): (a) $6.70; (b) $3.30; (c) $3.40; (d) $46.90