Question 915151
Let {{{ a }}} = pounds of hazelnuts needed
Let {{{ b }}} = pounds of cashews needed
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(1) {{{ a + b = 60 }}}
(2) {{{ ( 6.5a + 4.5b ) / 60 = 5.1 }}}
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(2) {{{ 6.5a + 4.5b = 5.1*60 }}}
(2) {{{ 6.5a + 4.5b = 306 }}}
(2) {{{ 65a + 45b = 3060 }}}
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Multiply both sides of (1) by {{{ 45 }}}
and subtract (1) from (2)
(2) {{{ 65a + 45b = 3060 }}}
(1) {{{ -45a - 45b = -2700 }}}
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{{{ 20a = 360 }}}
{{{ a = 18 }}}
and since
(1) {{{ a + b = 60 }}}
(1) {{{ b = 42 }}}
18 pounds of hazelnuts are needed
42 pounds of cashews are needed
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check:
You can do the check
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