5 marbles and 1 bead cost $21.40.
1 marble and 5 beads cost $25.40.
- 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 4 marbles and 4 beads.
(a)
5 marbles + 1 bead = 21.40 --- (1)
1 marble + 5 beads = 25.40 --- (2)
(1) + (2)
6 marbles + 6 beads = 21.40 + 25.40
6 marbles + 6 beads = 46.80 --- (3)
(3)
÷ 66 marbles + 6 beads = 46.80
1 marble + 1 bead = 46.80 ÷ 6
1 marble + 1 bead = 7.80 --- (4)
(b)
(2) - (4)
(1 marble + 5 beads) - (1 marble + 1 marble) = 25.40 - 7.80
1 marble - 1 marble + 5 beads - 1 bead = 17.60
4 beads = 17.60
1 bead = 17.60 ÷ 4 = 4.40
Cost of 1 bead = $4.40
(c)
Substitute 1 bead = 4.40 into (4).
1 marble + 1 bead = 7.80
1 marble + 4.40 = 7.80
1 marble = 7.80 - 4.40 = 3.40
Cost of 1 marble = $3.40
(d)
(4)
x 4 1 marble + 1 bead = 7.80
4 x (1 marble + 1 marble) = 4 x 7.80
4 marbles + 4 beads = 31.20
Cost of 4 marbles and 4 beads = $31.20
Answer(s): (a) $7.80; (b) $4.40; (c) $3.40; (d) $31.20