Question 1206418
S = number of shirts
T = number of ties.
x = cost of a tie.
x-14 = cost of a shirt.


you are given that:


x * T - (x-14) * S = 127.80
this means that the cost of the ties minus the cost of the shirts = 127.8.


x * T + (x-14) * S = 2385
this means that the cost of the ties plus the cost of the shirts = 2385.


add these two equations together to get 2 * x * T = 2512.8
solve for x * T to get x * T = 2512.8 / 2 = 1256.4 


since T = 2/3 * S, replace T with 2/3 * S to get x * 2/3 * S = 1256.4
multiply both sides of this equation by 3/2 to get x * S = 3/2 * 1256.4 = 1884.6


you now have x * T = 1256.4 and x * S = 1884.6


since x * T + (x-14) * S = 2385, and x * T = 1256.4, then (x-14) * S = 2385 - 1256.4 = 1128.6


you now have:


x * T = 1256.4
x * S = 1884.6
(x-14) * S = 1128.6


x * S - (x-14) * S = 1884.6 - 1128.6 = 756
combine like terms to get 14 * S = 756
solve for S to get S = 756 / 14 = 54


since T = 2/3 * S, then T = 2/3 * 54 = 36.


you now have S = 54 and T = 36.


in the equation x * T = 1256.4, solve for x to get x = 1256.4 / 36 = 34.9.


x - 14 must be equal to 34.9 minus 14 = 20.9.


x is the price of a tie = 34.9 and (x-14) is the price of a shirt = 20.9.


your original equation of x * T + (x - 14) * S = 2385 becomes:
34.9 * 36 + 20.9 * 54 = 2385 which becomes 2385 = 2385, confirming the values of x and S and T are good.


your solution is that you bought 36 ties at 34.9 each and 54 shirts at 20.9 each for a total price of 2385.


the total cost for the ties was 36 * 34.9 = 1256.4.
the total cost for the shirts was 54 * 20.9 = 1128.6.


you paid 1256.4 - 1128.6 = 127.8 more for the ties than you paid for the shirts.


answers to your questions are:


(a) How much did he pay for all the shirts?


he paid 1128.6 for all the shirts.


(b) How many ties did he buy?


he bought 36 ties.