SOLUTION: Hope you can help.... I"ve gone over this one a million times>>please help! One number is 7 less than another. If 4 times the smaller number plus 2 times the larger number i

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Question 52939This question is from textbook Beginning Algebra
: Hope you can help....
I"ve gone over this one a million times>>please help!
One number is 7 less than another. If 4 times the smaller number plus 2 times the larger number is 62. find the two numbers... I have the answer but I don't how to get the answer.....This question is from textbook Beginning Algebra

Answer by rchill(405) About Me  (Show Source):
You can put this solution on YOUR website!
Let x represent one number; then x-7 is the number that is 7 less. Because x-7 is less than x, it's the smaller number. We have 4 times the smaller number (i.e., x-7) represented as 4(x-7); two time the larger number (i.e., x) is represented as 2x. So now our equation is 4%28x-7%29%2B2x=62. Expanding the equation we get 4x-28%2B2x=62 which simplifies to 6x-28=62. Now just solve for x by adding 28 to both sides 6x=90 and then dividing both sides by 6 to get x=15. That means 15 is the larger of the two numbers, and the smaller number, represented by x-7, or 15-7, is 8. Therefore, the two numbers are 15 and 8. To check this, 4 times the smaller number (4*8=32) added to 2 times the larger (2*15=30) is 62 (32+30), and 8 is 7 less than 15. Therefore, 15 and 8 are correct!