Question

Bella spent 4/7 of her money on a dictionary and 3 identical books. She spent 1/6 of the remainder on a journal that cost $7. a) How much did she spend on the dictionary and 3 books? b) If 3/8 of the cost of the dictionary was the same as 1/2 of the total cost of 3 books, how much did each book cost?

Answer 1

a) 9.33$

b) 1.33$

Step-by-step explanation:

a)

To solve the problem, let's call

$m$ = the money that Bella has at the beginning

$d=$ the price of a dictionary

$b=$ the price of one book

$j=\ 7$ the price of the journal

Here, Bella spent 4/7 of her money to buy a dictionary and 3 books, so

$\frac{4}{7}m=d+3b$ (1)

Then she spent 1/6 of the remainder (which is $\frac{3}{7}m$) to buy the journal so

$\frac{3}{7}m=j=7$ (2)

So from this second equation we can find m, the money that she has at the beginning:

$m=\frac{7}{3}\cdot 7 =\frac{49}{3}=\ 16.3$

So the amount that she spent for the dictionary + the 3 books is

$\frac{4}{7}m = \frac{4}{7}\cdot \frac{49}{3}=\frac{28}{3}=\ 9.33$

b)

Here, we are told that

3/8 of the cost of the dictionary was the same as 1/2 of the total cost of 3 books

Which can be rewritten as an equation as follows:

$\frac{3}{8}d=\frac{1}{2}(3b)$

This means that we can rewrite the cost of the dictionary by re-arranging this equation as:

$d=\frac{8}{3}\cdot \frac{1}{2}(3b) =4b$

Substituting into eq.(1) of part a),

$\frac{4}{7}m=4b+3b\\\frac{4}{7}m=7b$

And from this, we can find b, the cost of each book:

$b=\frac{1}{7}\cdot \frac{4}{7}m=\frac{4}{49}\cdot \frac{49}{3}=\frac{4}{3}=\ 1.33$