SOLUTION: the greater of two numbers is 2 more than the lesser. the sum of 25 times the greater number and 50 times the lesser is 500. what are the number?

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Question 74901: the greater of two numbers is 2 more than the lesser. the sum of 25 times the greater number and 50 times the lesser is 500. what are the number?
Answer by cathieb1225(41) About Me  (Show Source):
You can put this solution on YOUR website!
the greater of two numbers is 2 more than the lesser. the sum of 25 times the greater number and 50 times the lesser is 500. what are the number?
x is the smaller number
x+2 is the bigger number
25(x+2) + 50x = 500
Multiply out the first term
25x+50 +50x = 500
Add like terms
75x + 50 = 500
Subtract 50 from both sides
75x +50 - 50 = 500 -50
75x = 450
Divide both sides by 75
75x/75=450/75
x=6
x+2=8
To check the solution, replace x and x+2 with the numbers found
25(8) +50(6)=500
200+300=500
500=500