Question 616419
Let {{{ a }}} = price of one of the cheaper pencils
Let {{{ b }}} = price of one of the dearer pencils
given:
{{{ 20a + 30b = 90 }}}
(1) {{{ 2a + 3b = 9 }}}
and
{{{ 30a + 20b = 90 - 5 }}}
{{{ 30a + 20b = 85 }}}
(2) {{{ 6a + 4b = 17 }}}
Multiply both sides of (1) by {{{ 3 }}}
and subtract (2) from (1)
(1) {{{ 6a + 9b = 27 }}}
(2) {{{ -6a - 4b = -17 }}}
{{{ 5b = 10 }}}
{{{ b = 2 }}}
and, since
(1) {{{ 2a + 3b = 9 }}}
(1) {{{ 2a + 3*2 = 9 }}}
(1) {{{ 2a = 9 - 6 }}}
(1) {{{ 2a = 3 }}}
(1) {{{ a = 1.5 }}}
1.5p is the  price of one of the cheaper pencils
2p is the price of one of the dearer pencils
check:
(2) {{{ 6a + 4b = 17 }}}
(2) {{{ 6*1.5 + 4*2 = 17 }}}
(2) {{{ 9 + 8 = 17 }}}
(2) {{{ 17 = 17 }}}
You can check (1)