Question

Robin has a table full of supplies that she will use to decorate picture frames. She decorated one frame with 3 buttons and 12 bows. On her other frames, she also wants to use 2 types of items on each picture frame, but only if the 2 items have the same unit rate as the items on the first frame. Which of the pairs of items could Robin use for the other frames?

Answer 1

The first frame uses 3 buttons and 12 bows, so the unit rate is 12 ÷ 3 = 4 bows per button (or 1 button per 4 bows). Any other pair must have the same ratio 1:4.

So acceptable pairs are those where the second item is 4 times the first item, e.g.
- 1 and 4
- 2 and 8
- 4 and 16
- 5 and 20
- 6 and 24
…or any (x, 4x).

To check any given pair (a, b), compute b ÷ a; if it equals 4 (or a ÷ b = 1/4) then that pair will work.