Question 1185105
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The cost of a packet of cookies is 2/5 the cost of a packet of nuts. Nic used 2/7 of his
money to buy 5 packets of cookies and 12 packets of nuts.
a) Using the same amount, how many packet of cookies can he buy instead?
b) With 3/7 of his money, how many packets of nuts can he then buy?
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<pre>
Since  "the cost of a packet of cookies is 2/5 the cost of a packet of nuts", 

we can think that one packet of cookies costs 2x, while one packet of nuts costs 5x.


Then the next statement  "Nic used 2/7 of his money to buy 5 packets of cookies and 12 packets of nuts"

allows us to write this equation


    5*(2x) + 12*(5x) = {{{(2/7)*M}}},      (1)


where M is the Nic's total money.


Simplify equation (1)


    10x + 60x = {{{(2/7)*M}}}        (2)

       70x    = {{{(2/7)*M}}}        (3)

      35*(2x) = {{{(2/7)*M}}}.       (4)


From the last equation (4),  you see that Nic can buy 35 packets of cookies for the same money  {{{(2/7)M}}}

instead of 5 packets of cookies and 12 packets of nuts.   It gives the  <U>ANSWER  to question (a)</U>.



Now, regarding packets of nuts of the question (b), we can deduce from equation (3)
    
    14*(5x) = {{{(2/7)*M}}}         (5)


which means that for {{{2/7}}} of his money Nic can buy 14 packets of nuts.


It makes clear, that for {{{3/7}}}  of his money, Nic can buy  {{{(14/2)*3}}} = 7*3 = 21 packet of nuts.


It is the  <U>ANSWER  to question (b)</U>.
</pre>

Solved and thoroughly explained.