Algebra homework

Question

How many multiples of 4 are there between 27 and 595?

A. 128

B. 144

C. 142

D. 150

Answer 1

Hi Leah,

Here are two ways you could solve this problem:

1. First answer the question how many multiples are there between 0 and 595?

We can find this number by dividing 595 by 4.

Then you need to subtract any multiples of 4 between 0 and 27. How many are there? (Hint: 6x4=24 but 7x4=28)

This difference will then give you the answer for the specified range of 27 to 595.

2. The other strategy you could use is to subtract 27 from 595 first, which would give you 568, and then find out how many multiples there are between 568 and 0, which you could do by dividing by 4. Think about how this relates to the first method and that you get the same result using each.

Remember that in each case your answer should be an integer aka a whole number. This is because you can't have a fractional "multiple" of a number. For example, you wouldn't say "I have 6.25 multiples of 4" for a given range -- rather you would have 6 multiples and would ignore that extra 0.25 part.

Cheers,

Holly

Answer 2

this can look at this problem as an arithmetic sequence going from 28 to 592 (first and last multiples of 4)

use the formula a_n=a₁+(n-1)d

a_n=last term, a₁=first term, d=common difference

592=28+(n-1)4

solve for n

592=28+4n-4

592=24+4n

568=4n

n=568/4

n=142

there are 142 multiples of 4 between 27 and 595 answer C.