Jose has a comic book collection that he keeps among 5 shelves with an equal number on each shelf. His father adds 20 comic books to the bottom shelf, so the shelf now has 125 books. How many total books are in his collection? Use algebra to solve the equation.(1 point
Let's say the number of comic books on each shelf is x.
Since there are 5 shelves with an equal number of comic books on each shelf, the total number of comic books on the shelves is 5x.
After his father adds 20 comic books to the bottom shelf, the number of comic books on that shelf becomes x + 20.
Thus, the total number of comic books on all the shelves is 5x + (x + 20) = 125.
Combining like terms, we get 6x + 20 = 125.
Subtracting 20 from both sides gives 6x = 105.
Dividing both sides by 6 gives x = 17.5.
Since x represents the number of comic books on each shelf and it is not possible to have a non-integer number of comic books, this means there is an error in the problem or the setup of the equation. Please check the problem statement and try again.
Let's assume the number of comic books on each shelf is x.
We know that there are 5 shelves in total, so the number of comic books in the collection before his father added 20 books can be calculated as 5x.
After his father added 20 books to the bottom shelf, that shelf now has 125 books. So the number of comic books on the bottom shelf is x + 20.
Therefore, the total number of comic books in his collection is 5x + (x + 20).
Now we can set up the equation:
5x + (x + 20) = total number of books
Simplifying the equation:
6x + 20 = total number of books
We know that the total number of books is 125, so we can now solve for x:
6x + 20 = 125
6x = 125 - 20
6x = 105
x = 105/6
x = 17.5
Since we cannot have a fraction of a book, we round down to the nearest whole number. Therefore, x = 17.
So the total number of comic books in Jose's collection is:
5x + (x + 20) = (5 * 17) + (17 + 20) = 85 + 37 = 122.
To solve this problem using algebra, we can follow these steps:
1. Let's assign a variable to the number of comic books on each shelf. Let's say x represents the number of comic books on each shelf.
2. Since there are 5 shelves, the total number of comic books on all shelves before his father added more would be 5x.
3. After his father added 20 comic books to the bottom shelf, the number of books on that shelf became x + 20.
4. Now we have the equation: 5x + (x + 20) = 125.
5. Simplify the equation by combining like terms: 6x + 20 = 125.
6. Next, isolate the variable on one side of the equation. Subtract 20 from both sides: 6x = 125 - 20.
7. Simplify the equation further: 6x = 105.
8. Finally, solve for x by dividing both sides of the equation by 6: x = 105 / 6.
9. Using a calculator, we find that x ≈ 17.5.
10. Since we can't have a half book, we can round down to the nearest whole number. So, x is approximately 17.
11. Now, we can find the total number of comic books in the collection by multiplying the number of books on each shelf (x) by the number of shelves (5): Total = 17 * 5.
12. The total number of comic books in Jose's collection is 85.