word problem in Algebra

Question

In Algebra 1 I am given the following word problem:

 

If 7,182 roses were killed in last night's frost, and this was 2 5/8 as many as the night before, how many roses were killed the night before?

 

Does 2 5/8 as many as equal more or less than 7,182? I am confused. Thank you for your help.

Answer 1

Hi James,

Yes, 2 5/8 is greater than one which means that more roses were killed last night than the night before.

Let the number of roses killed the night before be N and since 2 5/8 is equivalent to 21/8, then you need to find the following:

If 21/8 of N is equal to 7182, what is N? Putting this as an algebraic expression we have

 

 21/8 x N= 7182   or    21 N / 8  = 7182

 

Solving for N ( multiply both sides by 8)

 

21 N = 7182 x 8 = 57456 

( Dividing both sides by 21) N = 2736

2,736 roses were killed the night before. Good Luck

Answer 2

This was 2 5/8 as night before.

7182 =   2 5/8 · n

7128 = 21/8 · n       convert to improper fraction

57024 = 21n           multiply both sides by 8

4752 = n                 divide both sides by 21