Question

7. Siti spend 20% of her money on 1 bag and 2 T-shirts. The bag cost 3 times as much as each T-shirt. She spent 60% of the remaining money on a pair of shoes. (a) What was the ratio of the price of the bag to the price of 1 T-shirt to the price of the pair of shoes?

Answer 1

The ratio of the price of the bags and the amount of money Lynn spends are;

(a) 3 : 1 : 12

(b) $168

The steps used to find the ratio of the price of the bag to the price of 1 T-shirt to the price of the pair of shoes and the amount of money Lynn spends are as follows;

7. (a) Let x represent the initial amount of money, we get;

Amount Siti spends on a bag and 2 T-shirts = 0.2·x

The cost of the bag = 3 × The cost of each T-shirt

Therefore, we get;

3 × The cost of each T-shirt + 2 × The cost of each T-shirt = 0.2·x

5 × The cost of each T-shirt = 0.2·x

The cost of each T-shirt = 0.2·x/5

0.2·x/5 = 0.04·x

The cost of each T-shirt = 0.04·x

The cost of the bag = 3 × 0.04·x

3 × 0.04·x = 0.12·x

The cost of the bag = 0.12·x

The percentage of the remaining money she spends on a pair of shoes = 60%

Therefore, the amount she spends on a pair of shoes is; 60% × (x - 0.2·x)

60% × (x - 0.2·x) = 0.48·x

The amount she spends on a pair of shoes is; 0.48·x

The ratio of the price of the bag to the price of 1 T-shirt to the price of a pair of shoes is; 0.12·x : 0.04·x : 0.48·x = 3 : 1 : 12

(b) The percentage by which the price of shoes decreased = 25%

The price of the rest of the other items remain the same

The amount Lynn paid less for the items than Siti = $36

Therefore, the cost equivalent to the 25% decrease in shoe price = $36

25% of 0.48·x = $36

x = 36/(25% × 0.48)

x = 300

The amount of money with Siti, x = $300

The amount of money Siti spends is; 0.2·x + 0.48·x = 0.68·x

0.68·x = 0.68 × 300

0.68 × 300 = 204

Amount Siti spends = $204

Amount of money Lynn spends = $204 - $36

Amount of money Lynn spends = $168

Answer 2

(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

`(20)/(100)*100=\text{ \$}20`

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

`\begin{gathered} 1unit+3units=20 \\ 4units=20 \end{gathered}`

Divide both sides by 4 to find the value of 1 unit

`\begin{gathered} (4units)/(4)=(20)/(4) \\ 1unit=\text{ \$5} \end{gathered}`

The price of the T-shirt is $5

The price of the bag is 3 x 5 = $15

The remaining amount with her is

`\begin{gathered} \text{ R=\$}100-\text{ \$20} \\ R=\text{ \$}80 \end{gathered}`

She spent 60% of it on a pair of shoes, then find 60% of 80 dollars

`(60)/(100)*80=\text{ \$48}`

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

`B:T:SH=15:5:48`

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

`15^(\prime)+2*5+48=73\text{ parts}`

Lynn paid for

`\begin{gathered} 15+2*5+(48-(25)/(100)*48)= \\ 15+10+(48-12)= \\ 15+10+36=61\text{ parts} \end{gathered}`

The difference between 73 parts and 61 parts is 36 dollars

`\begin{gathered} 73\text{ parts}-61\text{ parts}=36 \\ 12\text{ parts}=36 \end{gathered}`

Divide both sides by 12

`\begin{gathered} \frac{12\text{ parts}}{12}=(36)/(12) \\ part=3 \end{gathered}`

Since Lynn paid a total of 61 parts, then multiply 61 by 3 to find the amount of money she paid

`Money=61*3=183`

She paid 183 dollars for the 4 items