SOLUTION: Solve: One number is 11 less than a second number. Twice the second number is 52 more than 4 times the first. Find the two numbers.

Question 146803: Solve:
One number is 11 less than a second number. Twice the second number is 52 more than 4 times the first. Find the two numbers.
Answer by 24HoursTutor.com(40) (Show Source): You can put this solution on YOUR website!
Let the two numbers be x and y. Now, we understand from the first sentence that the first number which we have assumed to be x is 11 less than the second number y. Which means that if we add eleven to the first number we will get the second number. Thus, we get the equation as :
x + 11 = y
Now, the second sentence tells us that twice the second number, y in our case is equal to 4 times the first number(x) and 52 more. So we have :
2y = 52 + 4x
Since we have an equation for y , we substitute it in this equation to get :
2(x+11) = 52 + 4x
2x + 22 = 52 + 4x
2x - 4x = 52 -22
- 2x = 30
x = 30 / -2
x = -15
Now, since we have the value of x, we can get the value of y by :
y = x + 11
y = -15 + 11
y = -4
Ans.: The first number is -15 and the second number is -4. You can cross check your answer by substituting the value in both the equations and seeing if they still hold true.
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