Question 1038941
Let {{{ a }}} = the cost of iced tea the 1st week
Let {{{ b }}} = the cost of a veggie burger the 1st week
Let {{{ c }}} = the cost of the fries the 1st week
----------------------------------------------
(1) {{{ a + b + c = 756 }}} ( in cents )
(2) {{{ c = 2a }}} ( in cents )
(3) {{{ 1.1a + 1.25b + c = 868 }}} ( in cents )
--------------------------------------
Multiply both sides of (3) by {{{ 100 }}}
(3) {{{ 110a + 125b + 100c = 86800 }}}
Multiply both sides of (1) by {{{ 100 }}}
and subtract () from (2)
(3) {{{ 110a + 125b + 100c = 86800 }}}
(1) {{{ -100a - 100b - 100c = -75600 }}}
------------------------------------
(4) {{{ 10a + 25b = 11200 }}}
Substitute (2) into (1)
(1) {{{ a + b + 2a = 756 }}}
(1) {{{ 3a + b = 756 }}}
Multiply both sides of (1) by {{{ 25 }}} and
subtract (4) from (1)
(1) {{{ 75a + 25b = 18900 }}}
(4) {{{ -10a - 25b = - 11200 }}}
----------------------------
{{{ 65a = 7700 }}}
{{{ a = 118.46 }}}
and
(2) {{{ c = 2a }}} 
(2) {{{ c = 236.92 }}}
and
(1) {{{ 3a + b = 756 }}}
(1) {{{ 3*118.46 + b = 756 }}}
(1) {{{ 355.38 + b = 756 }}}
(1) {{{ b = 400.62 }}}
-----------------------------
Convert to dollars since answers are in cents:
{{{ a = 1.18 }}}
{{{ b = 4.01 }}}
{{{ c = 2.37 }}}
The cost of iced tea the 1st week was $1.18
The cost of a veggie burger the 1st week was $4.01
The cost of the fries the 1st week was $2.37
------------------
check the answers:
(1) {{{ a + b + c = 7.56 }}} ( in dollars )
(1) {{{ 1.18 + 4.01 + 2.37 = 7.56 }}}
(1) {{{ 7.56 = 7.56 }}}
and
(2) {{{ c = 2a }}}
(2) {{{ 2.37 = 2*1.18 }}}
(2) {{{ 2.37 = 2.36 }}}
close enough
and
(3) {{{ 1.1a + 1.25b + c = 8.68 }}} ( in dollars )
(3) {{{ 1.1*1.18 + 1.25*4.01 + 2.37 = 8.68 }}}
(3) {{{ 1.298 + 5.0125 + 2.37 = 8.68 }}}
(3) {{{ 8.6805 = 8.68 }}}
OK when rounded off