2 marbles and 1 bead cost $9.10.
1 marble and 2 beads cost $10.70.
- 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)
2 marbles + 1 bead = 9.10 --- (1)
1 marble + 2 beads = 10.70 --- (2)
(1) + (2)
3 marbles + 3 beads = 9.10 + 10.70
3 marbles + 3 beads = 19.80 --- (3)
(3)
÷ 3
3 marbles + 3 beads = 19.80
1 marble + 1 bead = 19.80 ÷ 3
1 marble + 1 bead = 6.60 --- (4)
Cost of 1 marble and 1 bead = $6.60
(b)
(2) - (4)
(1 marble + 2 beads) - (1 marble + 1 marble) = 10.70 - 6.60
1 marble - 1 marble + 2 beads - 1 bead = 4.10
1 bead = 4.10
Cost of 1 bead = $4.10
(c)
Substitute 1 bead = 4.10 into (4).
1 marble + 1 bead = 6.60
1 marble + 4.10 = 6.60
1 marble = 6.60 - 4.10 = 2.50
Cost of 1 marble = $2.50
(d)
(4)
x 4 1 marble + 1 bead = 6.60
4 x (1 marble + 1 marble) = 4 x 6.60
4 marbles + 4 beads = 26.40
Cost of 4 marbles and 4 beads = $26.40
Answer(s): (a) $6.60; (b) $4.10; (c) $2.50; (d) $26.40