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Question 106284This question is from textbook Algabra Structure and Method
: The difference of two integers is 9. Five times the smaller is 7 more than three times the larger. Find the numbers.
This question is from textbook Algabra Structure and Method
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website!
Let x=the larger integer
And let y=the smaller integer
Now we are told that x-y=9--------------------------eq1
We are also told that 5y=3x+7-----------------------eq2
From eq1, substitute x=y+9 into eq2 and we get:
5y=3(y+9)+7 get rid of parens
5y=3y+27+7 subtract 3y from both sides
5y-3y=3y-3y+27+7 collect like terms
2y=34 divide both sides by 2
y=17------------------the smaller integer
From eq1, x=9+y=9+17=26 --------the larger integer
CK
x-y=9
26-17=9
9=9
also
5y=3x+7
5*17=3*26+7
85=78+7
85=85
Another way to solve this problem:
Let x=the larger integer
Then x-9= the smaller integer
Now we are told that:
5(x-9)=3x+7 get rid of parens
5x-45=3x+7 subtract 3x from and add 45 to both sides
5x-3x-45+45=3x-3x+45+7 collect like terms
2x=52 divide both sides by 2
x=26----------------the larger integer
x-9=26-9=17---------------the smaller integer
Hope this helps----ptaylor
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