Question 1082706
Let {{{ a }}} = number of small sizes he sold
Let {{{ b }}} = number of medium sizes he sold
Let {{{ c }}} = number of large sizes he sold
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There are 3 unknowns, so 3 equations
are needed to solve
(1) {{{ a + b + c = 52 }}}
(2) {{{ b = 2c + 2 }}}
(3) {{{ .89a + 1.19b + 1.39c = 58.98 }}}
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(3) {{{ 89a + 119b + 139c = 5898 }}}
plug 2 into 1
(1) {{{ a + ( 2c + 2 ) + c = 52 }}}
(1) {{{ a = 50 - 3c }}}
Plug (1) and (2) into (3)
(3) {{{ 89*( 50 - 3c ) + 119*( 2c + 2 ) + 139c = 5898 }}}
(3) {{{ 4450 - 267c + 238c + 238 + 139c = 5898 }}}
(3) {{{ 377c - 267c = 5898 - 4450 - 238 }}}
(3) {{{ 110c = 1210 }}}
(3) {{{ c = 11 }}}
and
(2) {{{ b = 2c + 2 }}}
(2) {{{ b = 2*11 + 2 }}}
(2) {{{ b = 24 }}}
and
(1) {{{ a = 50 - 3c }}}
(1) {{{ a = 50 - 3*11 }}}
(1) {{{ a = 17 }}}
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17 = number of small sizes he sold
24 = number of medium sizes he sold
11 = number of large sizes he sold
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check answer:
(3) {{{ .89a + 1.19b + 1.39c = 58.98 }}}
(3) {{{ .89*17 + 1.19*24 + 1.39*11 = 58.98 }}}
(3) {{{ 15.13 + 28.56 + 15.29 = 58.98 }}}
(3) {{{ 58.98 = 58.98 }}}
OK 
You can check (1) and (2)