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%