Hannah and Francine have 120$ Hannah and Peter have 230$ Peter has 6x as much as France. How much money does Hannah have?

Question

I am helping my some with a word problem been sitting here for an hour racking my brain someone help. 

Answer 1

Here is how it would be done with algebra:

 

(1) H + F = 120

(2) H + P = 230

(3) P = 6F

 

Substitute (3) into (2) ----> H + 6F = 230        This will be equation (4)

 

Solve (1) for H ---> H = 120 - F       This will be equation (5)

 

Substitute (5) into (4) 120 - F + 6F = 230 ---> 120 + 5F = 230 ---> 5F = 110 ---> F = 22

 

So P = 6(22) = 132

And H = 120 - 22 = 98. So Hannah has $98.

 

Make sure the second equation still works: 98 + 132 = 230 Yes, so it checks.

 

For 5th grade level one strategy is "guess and check" and another is "make a table". Maybe try different values in a table. Make them make Hannah+Francine = 120 and Peter = 6xFrancine and keep trying until H + P = 230

 

Hannah      Francine         Peter (6xF)        Hannah & Francine         Hannah & Peter - want 230

30                 90                  540                            120                       but got 570, too big so try bigger for H

50                 70                  420                           120                        but got 470, still too big

80                 40                  240                           120                        but got 320, still too big

100               20                  120                           120                        now get 220 so too small

98                 22                  110                           120                        230 (I cheated though since I knew it was 98)