Comparing rates from a table, step by step

Two tables, two rates, and one question: which climbs faster?

The question
Ay = 10x, y dollars and x weeksBx258y102540AB

Which is greater?

A y = 10x, y dollars and x weeks B x: 2, 5, 8 y: 10, 25, 40

Ay = 10x, y dollars and x weeks
Bx: 2, 5, 8 y: 10, 25, 40
y = 10x, y dollars and x weeks10 per week
10 ÷ 2=5 per week
A 10B 5
greater:A
  1. 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.
  2. A: the number in front of x, which is already a rate per one week: 10. So A is 10 dollars per week.
  3. B: any column divided by its own x — 10 ÷ 2 = 5. So B is 5 dollars per week.
  4. 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.

  1. 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.

  2. 02

    A: the number in front of x, which is already a rate per one week: 10. So A is 10 dollars per week.

  3. 03

    B: any column divided by its own x — 10 ÷ 2 = 5. So B is 5 dollars per week.

  4. 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.