A math book costs $9 and a science book costs $7. If Steve spends all his money in the science books, he still has $6 left. However, if he buys the same number of math books, he needs another $8 more.
(a) How many books is Steve buying?
(b) How much money does he have?
Where are these answers coming from, and who is answering them????
Suppose he has $M, and he buys x books
M - 7x = 6
M - 9x = -8
subtract these
2x = 14
x = 7
M - 49 = 6
M = 55
So he has $55, and he buys 7 books
check: to buy 7 science books would cost $49 leaving him with $6, check!
to buy 7 math books would cost $63 , leaving him $8 short
Let's assume Steve is buying "x" number of books.
To find the number of books Steve is buying, we need to solve the following equations:
The amount of money Steve has after buying science books:
7x + 6
The amount of money Steve needs to buy math books:
9x + 8
Since we know that the amount Steve has after buying science books is $6, we can set up the following equation:
7x + 6 = 6
Solving the equation:
7x = 6 - 6
7x = 0
x = 0
However, this does not make sense since we cannot have zero books. Therefore, our assumption is incorrect.
Let's try another assumption and assume Steve is buying "y" number of books.
Now we can set up the second equation using the new assumption:
9y + 8 = 6
Subtracting 8 from both sides of the equation:
9y = 6 - 8
9y = -2
Dividing both sides of the equation by 9:
y = (-2/9)
Again, this does not make sense since we cannot have a fractional number of books. Therefore, our assumption is incorrect.
We need to assume a whole number of books, so let's try a new assumption and assume Steve is buying "z" number of books.
Now we can set up a new equation using the new assumption:
7z + 6 = 9z + 8
Subtracting 7z from both sides of the equation:
6 = 2z + 8 - 7z
6 = -5z + 8
Subtracting 8 from both sides of the equation:
-2 = -5z
Dividing both sides of the equation by -5 (to solve for z):
z = -2 / 5
Again, this result does not make sense since we cannot have a fractional number of books. Therefore, our assumption is incorrect.
Based on the given information, it seems there is no proper solution to determine the number of books Steve is buying. Additionally, we cannot determine the amount of money Steve has.
(a) To solve for the number of books Steve is buying, let's assume he is buying x books of each type.
The cost of x science books is 7x dollars. Since he spends all his money on science books and still has $6 remaining, we can set up the equation:
7x + 6 = total amount of money Steve has.
Now, let's consider the cost of buying x math books. The cost of x math books is 9x dollars. However, if he buys the same number of math books, he needs an additional $8, so we can set up another equation:
9x + 8 = total amount of money Steve has.
Since we know both equations are equal to the total amount of money Steve has, we can set them equal to each other:
7x + 6 = 9x + 8.
Now, let's solve for x:
7x - 9x = 8 - 6,
-2x = 2,
x = -1.
However, since we are looking for a positive number of books, we can discard this solution.
Therefore, there is no valid solution for the number of books Steve is buying.
(b) Similarly, since we have no valid solution for the number of books Steve is buying, we cannot determine how much money he has.
(a) Steve is buying 3 books.
(b) Steve has $15.