# Algebra Problem and Question

#### einstein

##### New member
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
einstein said:
161 - 7y - 5y = 5
161 - 2y = 5
Should be 161 - 12y = 5 : give yourself a good kick :shock:

#### einstein

##### New member
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
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
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
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