Question 520775: I cannot solve this problem. I know what the answer is because I used a process if elimination but donīt understand how to write the equation.
The sum of a number is 18. Three times the greater number exceeds four times the smaller number by 5. Find the numbers. The answers are 7 and 11.
Is there
Is there anyway to solve this problem without 2 variables as we havenīt been using two variables, only one.
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Yes, there is a way using only one variable!
Let a = the smaller number, then (18-a) = the larger number. Why, because:
a+(18-a) = 18 "The sum of the two numbers is 18".
Also, from the problem description, you have:
3(18-a) = 4a+5 "Three times the larger number exceeds four times the smaller number by 5. Simplify this equation.
54-3a = 4a+5 Add 3a to both sides.
54 = 7a+5 Now subtract 5 from both sides.
49 = 7a Finally, divide both sides by 7.
7 = a or a = 7 and 18-7 = 11
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