Homework help please!

Hi. I have a two sided math sheet, and neither sides make sense. I'll write out the first question from each side.


Mrs. Wang is 23 years older than her daughter. In 5 years, their ages will total 63. How old are they now?


And...

Find two consecutive integers whose sum is 45.

If anyone could write out the work for these so I could teach myself, I'd be forever grateful!

Thanks,
Shanelle

Number One:

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Let Mr's Wang's age be x and her daughter's be y.
Since Mrs. Wang is 23 years older than her daughter,

x=y+23

Since in 5 years, their ages will total 63,

x+5+y+5=63

Now, from the first equation, we can substitute in y+23 for x in the second.

y+23+5+y+5=63

2y+33=63

2y=30

y=15

x=15+23

x=38

So, Mrs. Wang is 38; her daughter is 15.

Number Two:

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Let the smaller number be a. Since they're consecutive, the larger one is a+1. Thus,

a+a+1=45

2a+1=45

2a=44

a=22

Thus, the numbers are 22 and 23.