Angela spent 3/8 of her money on 3 books and 9 pens. The cost of
each book is 4 times the cost of each pen. She bought some more
books with 4/7 of her remaining money.
(a) How many pens can Angela buy with 3/8 of her money?
(b) How many books did Angela buy altogether?
(c) If each pen cost $1.50, how much money did Angela have at first?
To solve this problem, let's break it down step by step:
(a) To find out how many pens Angela can buy with 3/8 of her money, we first need to determine the total cost of the 3 books and 9 pens.
Let's assume the cost of each pen is 'p' dollars. Since the cost of each book is 4 times the cost of each pen, then the cost of each book would be 4p dollars.
The total cost of the 3 books would be 3 * 4p = 12p dollars.
The total cost of the 9 pens would be 9 * p = 9p dollars.
The total cost of the books and pens together would be 12p + 9p = 21p dollars.
Since Angela spent 3/8 of her money on these items, we can set up the equation:
3/8 * Total Money = 21p
To find how many pens she can buy, we need to solve for 'p':
Total Money = (8/3) * 21p
Total Money = 56p
Now, let's calculate the number of pens she can buy. If each pen costs $1.50, then we can divide the total money by the cost of each pen:
Number of Pens = Total Money / Cost per Pen
Number of Pens = 56p / $1.50
(b) To determine the number of books Angela bought altogether, we can use the information that she bought some more books with 4/7 of her remaining money. Let's assume she bought 'b' books.
The cost of each additional book would still be 4p dollars. So the total cost of the additional books would be:
Total Cost of Additional Books = b * 4p
The remaining money after buying the first set of books and pens would be (1 - 3/8) = 5/8 of the original money.
So, the money spent on the additional books would be (4/7) * (5/8) of Angela's initial money. We can set up another equation:
Total Money - initial money = (4/7) * (5/8) * initial money
56p - initial money = (20/56) * initial money
To find 'b', we can solve this equation:
b * 4p = (20/56) * initial money
(c) To find out how much money Angela had initially, we can use the information we obtained from part (b).
Now, we can solve equations (a) and (b) simultaneously to find the numerical values for the number of pens (a), the number of books (b), and Angela's initial money (c).