algebra confused simple question

[bronx.system]

Im having trouble with the worded questions eg

One number is 13 less than the other. Their sum is 45. What are the numbers?

My working
i have been messing around with numbers and not sure why this works can someone please just explain each step please

m + ( m - 13) = 45
2m - 13 = 45 (this part makes me think i wrote it wrong because the above means it should be 2m - 13m = 45?)
2m = 58
m = 29

then i just subtract 29 from 45 and get 16
29 + m = 45
m = 16

so numbers are 16, 29
i checked answer but im sure my working is flawed can someone point out where ><

 

[Deleted member 4993]

Im having trouble with the worded questions eg

One number is 13 less than the other. Their sum is 45. What are the numbers?

My working
i have been messing around with numbers and not sure why this works can someone please just explain each step please

Let the larger # = m

m + ( m - 13) = 45
2m - 13 = 45 ....................................This is correct

(shouldnt it be 2m + 13m = 45)? ....................this question makes me nervous! How do you think m + (m-13) = 45 becomes 2m + 13m = 45?

It is very important to understand how m + (m - 13) becomes 2m - 13.
2m = 58
m = 29

then i just subtract 29 from 45 and get 16
29 + m = 45
m = 16

so numbers are 16, 29

is my working out correct?

Correct - except the comments above.

You can verify your answer by checking the given conditions.

One number is 13 less than the other. 29 - 16 = 13 ................................Checks

Their sum is 45. 29 + 16 = 45 ..............................................................Checks

Since it satisfes the given conditions, your answers are ost probably correct.

 

[serds]

.

m = number 1
n = number 2, which is 13 less than number 1, so it is (m-13)

2m - 13 = 45 (this part makes me think i wrote it wrong because the above means it should be 2m - 13m = 45?)

This is correct. That is a simple addition.
If you multiply them it would be:
m*(m-13)= m*m-13*m = m²-13m
if you add them it is:
m+(m-13) = m+m-13 = 2m-13

then i just subtract 29 from 45 and get 16
29 + m = 45
m = 16

or: n = m-13 = 29-13 =16
and 29+16=45
so that's the proof that it is correct

so numbers are 16, 29
i checked answer but im sure my working is flawed can someone point out where ><

 

[bronx.system]

thanks for reply

i think i understand now

m + ( m - 13) = 45
EDIT:

thanks thats what i was confused about

the parentheses confused me i thought i had to multiple :mrgreen:

all good thanks all