Which rate is greater?, step by step

Which one is faster?

The question
A42 dollars in 7 weeksBy = 11x, y dollars and x weeksAB

Which is greater?

A 42 dollars in 7 weeks B y = 11x, y dollars and x weeks

A42 dollars in 7 weeks
By = 11x, y dollars and x weeks
42 ÷ 7=6 per week
y = 11x, y dollars and x weeks11 per week
A 6B 11
greater:B
  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: 42 ÷ 7 = 6. So A is 6 dollars per week.
  3. B: the number in front of x, which is already a rate per one week: 11. So B is 11 dollars per week.
  4. Now they can be compared: A is 6 and B is 11 per week, so B is greater. Notice that A had the bigger number written on it — 42 — 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: 42 ÷ 7 = 6. So A is 6 dollars per week.

  3. 03

    B: the number in front of x, which is already a rate per one week: 11. So B is 11 dollars per week.

  4. 04

    Now they can be compared: A is 6 and B is 11 per week, so B is greater. Notice that A had the bigger number written on it — 42 — and is the slower one. The size of what is printed says nothing until it is a rate.