5 marbles and 1 bead cost $13.40.
1 marble and 5 beads cost $21.40.
- 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 7 marbles and 7 beads.
(a)
5 marbles + 1 bead = 13.40 --- (1)
1 marble + 5 beads = 21.40 --- (2)
(1) + (2)
6 marbles + 6 beads = 13.40 + 21.40
6 marbles + 6 beads = 34.80 --- (3)
(3)
÷ 66 marbles + 6 beads = 34.80
1 marble + 1 bead = 34.80 ÷ 6
1 marble + 1 bead = 5.80 --- (4)
(b)
(2) - (4)
(1 marble + 5 beads) - (1 marble + 1 marble) = 21.40 - 5.80
1 marble - 1 marble + 5 beads - 1 bead = 15.60
4 beads = 15.60
1 bead = 15.60 ÷ 4 = 3.90
Cost of 1 bead = $3.90
(c)
Substitute 1 bead = 3.90 into (4).
1 marble + 1 bead = 5.80
1 marble + 3.90 = 5.80
1 marble = 5.80 - 3.90 = 1.90
Cost of 1 marble = $1.90
(d)
(4)
x 7 1 marble + 1 bead = 5.80
7 x (1 marble + 1 marble) = 7 x 5.80
7 marbles + 7 beads = 40.60
Cost of 7 marbles and 7 beads = $40.60
Answer(s): (a) $5.80; (b) $3.90; (c) $1.90; (d) $40.60