a) 9.33$
b) 1.33$
Step-by-step explanation:
a)
To solve the problem, let's call
[tex]m[/tex] = the money that Bella has at the beginning
[tex]d=[/tex] the price of a dictionary
[tex]b=[/tex] the price of one book
[tex]j=\$7[/tex] the price of the journal
Here, Bella spent 4/7 of her money to buy a dictionary and 3 books, so
[tex]\frac{4}{7}m=d+3b[/tex] (1)
Then she spent 1/6 of the remainder (which is [tex]\frac{3}{7}m[/tex]) to buy the journal so
[tex]\frac{3}{7}m=j=7[/tex] (2)
So from this second equation we can find m, the money that she has at the beginning:
[tex]m=\frac{7}{3}\cdot 7 =\frac{49}{3}=\$16.3[/tex]
So the amount that she spent for the dictionary + the 3 books is
[tex]\frac{4}{7}m = \frac{4}{7}\cdot \frac{49}{3}=\frac{28}{3}=\$9.33[/tex]
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:
[tex]\frac{3}{8}d=\frac{1}{2}(3b)[/tex]
This means that we can rewrite the cost of the dictionary by re-arranging this equation as:
[tex]d=\frac{8}{3}\cdot \frac{1}{2}(3b) =4b[/tex]
Substituting into eq.(1) of part a),
[tex]\frac{4}{7}m=4b+3b\\\frac{4}{7}m=7b[/tex]
And from this, we can find b, the cost of each book:
[tex]b=\frac{1}{7}\cdot \frac{4}{7}m=\frac{4}{49}\cdot \frac{49}{3}=\frac{4}{3}=\$1.33[/tex]
