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1. from the problem we can deduce the following:
x+y=125
x-y=25
2. solve the second equation for y by:
a. adding y to both sides
x-y+y=25+y
the y's on the left cancel out leaving:
x=25+y
3. substitute the above equation into the original equation from the problem:
25+y+y=125
a. combine like terms on the left yields:
25+2y=125
b. to isolate y subtract 25 from each side leaving:
25-25+2y=125-25
c. simplify
the 25's on the left cancel out leaving:
2y=100
c. divide both sides by 2
2y/2=100\2
d. simplify
y=50
4. substitute the above value for y in the equation:
x+y=125
this gives us
x+50=125
5. subtract 50 from each side to isolate x leaving:
x+50-50=125-50
6. simplify:
x=75 Therefore, the bigger number is 75.
CHECK
plug both values into each equation and see if it is a true statement:
75+50=125
125=125
75-50=25
25=25
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