2 Story Probs: mixing grades of tea, grades of antifreeze

[posenkid88]

1) A grocer is mixing tea. The 1st tea at $6 per pound and the 2nd tea at $8 per pound. He wans to obtain 144 pounds of tea worth $7.50 per pound. Need to find out how much tea of each should be used.

2)How many quarts of water must be added to 5 quarts of 80% anti-freeze to make a 50% anti-freeze solution.

Thanks to anyone who can help!!!

 

[Denis]

HINT:

a @ x
b @ y
======
a+b @ z

z = (ax + by) / (a + b)

 

[posenkid88]

What problem is the hint for?

 

[Denis]

BOTH!

1) A grocer is mixing tea. The 1st tea at $6 per pound and the 2nd tea at $8 per pound. He wans to obtain 144 pounds of tea worth $7.50 per pound. Need to find out how much tea of each should be used.
a @ 6
144-a @ 8
========
144 @ 7.5
[6a + 8(144-a)] / 144 = 7.5 ; solve for a


2)How many quarts of water must be added to 5 quarts of 80% anti-freeze to make a 50% anti-freeze solution.
a @ 0
5 @ 80
=======
a+5 @ 50
[0a + 5(80)] / (a+5) = 50 ; solve for a

You should now be an expert "mixer" :wink:

 

[posenkid88]

36lbs of $6 tea, and 108lbs of $8 tea. Is that correct???

Porblem 2 cant figure out how t solve that.

 

[Denis]

[0a + 5(80)] / (a+5) = 50 ; solve for a

Why are you having problems with that one...easier than the other one!

zero times a = zero, right? So:
400 / (a+5) = 50