Algebra Problem and Question

einstein

New member
Joined
Sep 14, 2010
Messages
46
The sum of two numbers is 23. Seven times the first number less five times the second number is equal to 5. What are the two numbers?

Now, i have worked this out and the numbers i get equal 23 but are not the numbers given as the answer in the book. Take a look:

x + y = 23
7x - 5y = 5
7(23 - y) - 5y = 5
161 - 7y - 5y = 5
161 - 2y = 5
2y = 156
y = 78

Put the numbers into the equation: -55 + 78 = 23

So the answer i get appears to be correct because it works. But like i said, the answer in the back of the book is 10 + 13 = 23

So where did i go wrong? And if algebra lead me to my answer (-55 + 78 = 23) which makes the equation true, why can't my answer be the right answer?
 

Denis

Senior Member
Joined
Feb 17, 2004
Messages
1,445
einstein said:
161 - 7y - 5y = 5
161 - 2y = 5
Should be 161 - 12y = 5 : give yourself a good kick :shock:
 

einstein

New member
Joined
Sep 14, 2010
Messages
46
Denis said:
einstein said:
161 - 7y - 5y = 5
161 - 2y = 5
Should be 161 - 12y = 5 : give yourself a good kick :shock:
Why? Why does the minus belong to the "7y" to make it a "-7y"?
 

Mrspi

Senior Member
Joined
Dec 17, 2005
Messages
2,128
einstein said:
The sum of two numbers is 23. Seven times the first number less five times the second number is equal to 5. What are the two numbers?

Now, i have worked this out and the numbers i get equal 23 but are not the numbers given as the answer in the book. Take a look:

x + y = 23
7x - 5y = 5
7(23 - y) - 5y = 5
161 - 7y - 5y = 5<-----Error is here. Remember that the algebraic definition of subtraction is this:

Subtracting a number is the same as ADDING THE OPPOSITE of the number.

161 - 7y - 5y = 5
Rewrite the subtractions as adding the opposite:
161 + (-7y) + (-5y) = 5
Now, do the addition of the like terms. (-7y) + (-5y) is the same thing as -12y

161 - 2y = 5
2y = 156
y = 78

Put the numbers into the equation: -55 + 78 = 23

So the answer i get appears to be correct because it works. But like i said, the answer in the back of the book is 10 + 13 = 23

So where did i go wrong? And if algebra lead me to my answer (-55 + 78 = 23) which makes the equation true, why can't my answer be the right answer?
 

Subhotosh Khan

Super Moderator
Staff member
Joined
Jun 18, 2007
Messages
18,134
einstein said:
Denis said:
einstein said:
161 - 7y - 5y = 5
161 - 2y = 5
Should be 161 - 12y = 5 : give yourself a good kick :shock:
Why? Why does the minus belong to the "7y" to make it a "-7y"?
That needs face-to-face discussion with your teacher - you need to "modify" your understanding of negative numbers.
 

Denis

Senior Member
Joined
Feb 17, 2004
Messages
1,445
einstein said:
Denis said:
einstein said:
161 - 7y - 5y = 5
161 - 2y = 5
Should be 161 - 12y = 5 : give yourself a good kick :shock:
Why? Why does the minus belong to the "7y" to make it a "-7y"?
You have $10. You buy an item for $3 and another item for $2 ; you got $5 left, right?
10 - 3 - 2 = 10 - (3 + 2) = 10 - 5 = 5
161 - 7y - 5y is just as simple : 161 - (7y + 5y) = 161 - 12y ; make SURE you grasp that
 
Top