Grade 9 : Math : Word Problem

 John mixed cashews and almonds.

 John bought 4 pounds of almonds for a total of $22

The cost per pound for cashews is 60% more than the cost per pound for almonds.

John bought enough cashews that, when he mixed them with the almonds, the mixture had a value of $6.50 per pound.

What percent of the mixture, by weight, were cashews?

a) 20%       b) 25%   c) 30%  d) 35%

Answer

Given

4 Pounds of almonds cost = $22

1 Pound of almonds cost = 22/4 = $5.50

Also given,

 The cost per pound for cashews is 60% more than the cost per pound for almonds

which implies

1 pound of Cashews = 60% of 1pound almonds + cost of 1pound almonds 

                                   = 60% of 5.50 + 5.50

                                   = 0.60 * 5.50 + 5.50

                                   = 3.3 + 5.50

                                   = $ 8.80

 the mixture had a value of $6.50 per pound.

that is, 5.50 almonds + 8.80 Cashews = 6.50

Now, let's take each option one by one and substitute that in the above equation 

a) if cashew is 20% then almond must be 80%

5.50 * 80% + 8.80*20% = 6.50

5.50 * 0.8 + 8.80 * 0.2 = 6.50

     4.4       +  1.76     =  6.50

      6.16  = 6.50 ( Not True )

let's move on to option b)  if cashew is 25% then almond must be 75%

5.50 * 75% + 8.80*25% = 6.50

5.50 * 0.75 + 8.80 * 0.25 = 6.50

    4.125       +  2.2    =  6.50

      6.325  = 6.50 ( Not True )

let's move on to option c)  if cashew is 30% then almond must be 70%

5.50 * 70% + 8.80*30% = 6.50

5.50 * 0.70 + 8.80 * 0.30 = 6.50

    3.85      +  2.64     =  6.50

      6.49  = 6.50 ( which is very close)

let's move on to option d)  if cashew is 35% then almond must be 65%

5.50 * 65% + 8.80*35% = 6.50

5.50 * 0.65 + 8.80 * 0.35 = 6.50

    3.575      +    3.08   =  6.50

      6.655   = 6.50 ( Close but option is more close than this )

Hence the answer is option c) 30%