Question 943192
You don't say what {{{ x }}} and {{{ y }}} mean
I would define them as:
Let {{{ x }}} = the number of minutes the machine
spends making bowls
Let {{{ y }}} = the number of minutes the machine 
spends making plates
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Then my equations would be:
(1) {{{ 25*(x/3) +20y = 4400 }}} ( changing dollars to cents )
(2) {{{ x + y = 480 }}}
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(1) {{{ 25x + 60y = 13200 }}}
(1) {{{ 5x + 12y = 2640 }}}
Multiply both sides of (2) by {{{ 5 }}} and
subtract (2) from (1)
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(1) {{{ 5x + 12y = 2640 }}}
(2) {{{ -5x - 5y = -2400 }}}
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{{{ 7y = 240 }}}
{{{ y = 34.286 }}}
and
(2) {{{ x + y = 480 }}}
(2) {{{ x = 445.714 }}}
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{{{ x/3 = 148.571 }}}
It looks like the machine makes
148 bowls and 34 plates
( can't make fractions of them )
check:
(1) {{{ 25*(x/3) +20y = 4400 }}}
(1) {{{ 25*148.571 +20*34.286 = 4400 }}}
(1) {{{ 3714.28 + 685.72 }}}
(1) {{{ 4400 = 4400 }}}
and
(2) {{{ x + y = 480 }}}
(2) {{{ 445.714 + 34.286 = 480 }}}
(2) {{{ 480 = 480 }}}
OK
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Check my math, assumptions, and conclusions
carefully. I have been WAY off base before.