(a)
Since she spent 20% of her money on 1 bag and 2 T-shirts
Then we will assume that she had 100 dollars
20% of 100 dollars is
[tex]\frac{20}{100}\times100=\text{ \$}20[/tex]Since the cost of the bag is 3 times the cost of the T-shirt
That means if the T-shirt is 1 unit, then the bag is 3 units
[tex]\begin{gathered} 1unit+3units=20 \\ 4units=20 \end{gathered}[/tex]Divide both sides by 4 to find the value of 1 unit
[tex]\begin{gathered} \frac{4units}{4}=\frac{20}{4} \\ 1unit=\text{ \$5} \end{gathered}[/tex]The price of the T-shirt is $5
The price of the bag is 3 x 5 = $15
The remaining amount with her is
[tex]\begin{gathered} \text{ R=\$}100-\text{ \$20} \\ R=\text{ \$}80 \end{gathered}[/tex]She spent 60% of it on a pair of shoes, then find 60% of 80 dollars
[tex]\frac{60}{100}\times80=\text{ \$48}[/tex]Then the price of the pair of shoes is $48
Now we can find the ratio between the price of the bag to the price of 1 T-shirt to the price of the pair of shoes
[tex]B:T:SH=15:5:48[/tex]The answer is
Bag: T-shirt: Shoes = 15: 5: 48
(b)
Since Lynn took a discount of 25% on the shoes
Since she bought the same 4 items
Since she paid less than Siti by 36 dollars
This 25% will be equivalent to 36 dollars
Siti paid for
[tex]15^{\prime}+2\times5+48=73\text{ parts}[/tex]Lynn paid for
[tex]\begin{gathered} 15+2\times5+(48-\frac{25}{100}\times48)= \\ 15+10+(48-12)= \\ 15+10+36=61\text{ parts} \end{gathered}[/tex]The difference between 73 parts and 61 parts is 36 dollars
[tex]\begin{gathered} 73\text{ parts}-61\text{ parts}=36 \\ 12\text{ parts}=36 \end{gathered}[/tex]Divide both sides by 12
[tex]\begin{gathered} \frac{12\text{ parts}}{12}=\frac{36}{12} \\ part=3 \end{gathered}[/tex]Since Lynn paid a total of 61 parts, then multiply 61 by 3 to find the amount of money she paid
[tex]Money=61\times3=183[/tex]She paid 183 dollars for the 4 items
