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