Question 1197227

Let: 

{{{x}}}=hazelnuts

{{{y}}}=peanuts

 

Therefore:

    {{{x + y = 24}}}...........eq.1

    {{{7.00x + 4.50y = 5.54 *24}}}

{{{7.00x + 4.50y = 132.96}}}.........eq.2


By using the substitution method:

   {{{y = 24 - x}}}.............eq. 1a  (from the first equation)

Substituting this value of {{{x}}} into the 2nd equation we can solve for {{{y}}}:

    {{{7.00x + 4.50( 24 - x) = 132.96 }}}

  {{{7.00x + 108 - 4.5x= 132.96 }}}

     {{{2.5x + 108=132.96 }}}

    {{{2.5x =132.96 - 108}}}

      {{{x =24.96/2.5}}}

  {{{x =9.984}}}.........round  to the nearest pounds

 {{{x =10}}}

Putting this value of {{{x}}} into the eq.1a we can solve for {{{y}}}:

     {{{y = 24 - 10}}}.............eq. 1a  

      {{{y = 14 }}}

     

Therefore the answer is:

 {{{10}}} pounds of hazelnut 

{{{14}}} pounds of peanuts