A bag of mixed nuts contains cashews, pistachios, and almonds.

Question

A bag of mixed nuts contains cashews, pistachios, and almonds. There are 2000 total nuts in the bag, and there are 300 fewer almonds than pistachios. Cashews weigh 1 g, pistachios weigh 2 g, and almonds weigh 4 g. If the bag weighs 2.6 kg, find out how many of each type of nut is in the bag.

Answer 1

C+ P + A = 2000

A = P-300

C + 2P + 4A = 2600 <--- 1 kg = 1000 grams

subtitutes the 2nd equation into the 1st and 3rd equations,

so as to eliminate A

C + P + P-300 = 2000

C + 2P + 4(P-300) = 2600

155

simplifies (lots of algebra skipped here...

left for you to verify)

C + 2P = 2300

C + 6P = 3800

subtracts BOTTOM - TOP:

4P = 1500

P = 375

Then C + 2p = 2300

C + 750 = 2300

C = 1550

this forces A = 2000 - 375 - 1550 = 75

checks the weights!

1*1550 + 2*375 + 4*75 =

1550 + 750 + 300 =

2300 + 300 =

2600

yes it checks

1550 cashews

375 pistachios

75 almonds