5 marbles and 1 sticker cost $20.10.
1 marble and 5 stickers cost $9.30.
- Find the cost of 1 marble and 1 sticker.
- Find the cost of 1 sticker.
- Find the cost of 1 marble.
- Find the cost of 8 marbles and 8 stickers.
(a)
5 marbles + 1 sticker = 20.10 --- (1)
1 marble + 5 stickers = 9.30 --- (2)
(1) + (2)
6 marbles + 6 stickers = 20.10 + 9.30
6 marbles + 6 stickers = 29.40 --- (3)
(3)
÷ 66 marbles + 6 stickers = 29.40
1 marble + 1 sticker = 29.40 ÷ 6
1 marble + 1 sticker = 4.90 --- (4)
(b)
(2) - (4)
(1 marble + 5 stickers) - (1 marble + 1 marble) = 9.30 - 4.90
1 marble - 1 marble + 5 stickers - 1 sticker = 4.40
4 stickers = 4.40
1 sticker = 4.40 ÷ 4 = 1.10
Cost of 1 sticker = $1.10
(c)
Substitute 1 sticker = 1.10 into (4).
1 marble + 1 sticker = 4.90
1 marble + 1.10 = 4.90
1 marble = 4.90 - 1.10 = 3.80
Cost of 1 marble = $3.80
(d)
(4)
x 8 1 marble + 1 sticker = 4.90
8 x (1 marble + 1 marble) = 8 x 4.90
8 marbles + 8 stickers = 39.20
Cost of 8 marbles and 8 stickers = $39.20
Answer(s): (a) $4.90; (b) $1.10; (c) $3.80; (d) $39.20