SOLUTION: The sum of two numbers is 22. Five times one number is equal to 6 times the second number. Find the numbers. x + y = 22 5x = 6y I believe these are the correct equations, bu

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Question 113504This question is from textbook Arithmetic and algebra again
: The sum of two numbers is 22. Five times one number is equal to 6 times the second number. Find the numbers.
x + y = 22
5x = 6y
I believe these are the correct equations, but I am drawing blanks. I know the answer is x=12, y=10 just from the second equation, but I cannot do it algebraically. This question is from textbook Arithmetic and algebra again

Found 2 solutions by ptaylor, checkley71:
Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website!
YOUR EQUATIONS ARE CORRECT!!! GOOD WORK!!!! NOW THE HARD PART IS BEHIND YOU.
Let x=one number
And y=the other
x + y = 22 -----eq1
5x = 6y ----eq2
Multiply eq1 by 5:
5x+5y=120-------------------eq1a
Next, substitute 5x=6y into eq1a:
6y+5y=120 collect like terms
11y=120 divide both sides by 11
y=10----------------------------------------the other number
substitute y=10 into eq2
5x=6*10=60 divide both sides by 5
x=12------------------------------------one number
ANOTHER WAY:
Let x=one number
Then 22-x=the other
Now we are told that:
5x=6(22-x) get rid of parens
5x=132-6x add 6x to both sides
5x+6x=132-6x+6x collect like terms
11x=132 divide both sides by 11
x=12 ------------------one number
22-x=22-12=10------------------the other number

Hope this helps-------------------ptaylor

Answer by checkley71(8403) (Show Source):
You can put this solution on YOUR website!
X+Y=22 OR X=22-Y
5X=6Y
NOW REPLACE X IN THIS EQUATION WITH (22-Y) & SOLVE FOR Y;
5(22-Y)=6Y
110-5Y=6Y
11Y=110
Y=10 ANSWER.
X+10=22
X=22-10
X=12 ANSWER.