Question

Matt took clothes to the cleaners three times last month.​ First, he brought 4 shirts and 2 pairs of slacks and paid $17.94 Then he brought 6 shirts, 2 pairs of​ slacks, and 1 sports coat and paid $28.41. ​Finally, he brought 5 shirts and 1 sports coat and paid $14.94 How much was he charged for each​ shirt, each pair of​ slacks, and each sports​ coat?

Matt was charged $____for each​ shirt, $___for each pair of​ slacks, and $___for each sports coat.

Answer 1

Answer :-

Let , Shirts = a

Pairs of slacks = b

Sports Coat = c

​First, he brought 4 shirts and 2 pairs of slacks and paid $17.94 the equation 1 is -

=> 4a + 2b = $17.94 ......... equation 1

=> 2b = - 4a + 17.94

=> b= (- 4a + 17.94)/2

=>b= - 2a + 8.97

He brought 6 shirts, 2 pairs of​ slacks, and 1 sports coat and paid $28.41 the equation 2

=> 6a + 2b + 1c = $28.41. .......... equation 2

Put the value of b = - 2a + 8.97 in equation 2

=> 6a + 2(- 2a + 8.97) + 1c = $28.41

=> 6a - 4a + 17.94 + 1c = 28.41

=> 1c = 28.41 - 17.94 - 2a

=> c = 10.47 - 2a

He brought 5 shirts and 1 sports coat and paid $14.94 the equation 3 -

=> 5a + 1c = $14.94 .................... equation 3

Put the value of c = 10.47 - 2a in equation 2

=> 5a + 1(10.47 - 2a ) = $14.94

=> 5a + 10.47 - 2a = 14.94

=> 3a = 14.94 - 10.47

=> a = 4.47/3

=> a = $ 1.49

Now we put the value of a = $1.49 in equation 1

=> 4($1.49 ) + 2b = $ 17.94

=> $5.96 + 2b = $17.94

=> b =( $ 17.94 - $5.96)/2

=> b = 5.99

Now we put the value of a = $1.49 in equation 3

=> 5($1.49) + 1c = $14.94

=> $7.45 + 1c = $ 14.94

=> c = $14.94 - $7.45

=> c = 7.49

Matt was charged _$1.49​​​​​ for each​ shirt , $5.99  for each pair of​slacks, and $7.49 for each sports coat.