Comparing rates from a table, step by step
Two tables, two rates, and one question: which climbs faster?
Which is greater?
A y = 10x, y dollars and x weeks B x: 2, 5, 8 y: 10, 25, 40
- These two are written in different ways, so there is nothing to compare yet — the numbers on the page are not the same kind of number. Turn each one into a rate PER ONE week first, and do not look at which looks bigger until you have.
- A: the number in front of x, which is already a rate per one week: 10. So A is 10 dollars per week.
- B: any column divided by its own x — 10 ÷ 2 = 5. So B is 5 dollars per week.
- Now they can be compared: A is 10 and B is 5 per week, so A is greater. Notice that B had the bigger number written on it — 40 — and is the slower one. The size of what is printed says nothing until it is a rate.
How it works.
- 01
These two are written in different ways, so there is nothing to compare yet — the numbers on the page are not the same kind of number. Turn each one into a rate PER ONE week first, and do not look at which looks bigger until you have.
- 02
A: the number in front of x, which is already a rate per one week: 10. So A is 10 dollars per week.
- 03
B: any column divided by its own x — 10 ÷ 2 = 5. So B is 5 dollars per week.
- 04
Now they can be compared: A is 10 and B is 5 per week, so A is greater. Notice that B had the bigger number written on it — 40 — and is the slower one. The size of what is printed says nothing until it is a rate.