Problem Solving

Hi

I came across this problem in a high school text book. Appreciate if someone can explain the solution.

Q: What quantites of silver 60% and 82% pur must be mixed together to give 12 ounces of silver 70% pure.

A: x= no.of ounces of 60% silver
y= no.of ounces of 82% silver


x + y =12
(0.6)x+(0.82)y = (0.7)12

Solving the above 2 eqtn.s, x= 72/11 & y= 60/11

My question is why use 2 unknowns x & y? I had tried to solve it with just one unknown as follows:

(0.6)x + (0.82) (12-x) = (0.7)12

Solving the above eqtn., my answer was x = 6

It would be helpful if someone can explain.

Thanks
Pavithra

pavithra wrote:
My question is why use 2 unknowns x & y? I had tried to solve it with just one unknown as follows:

(0.6)x + (0.82) (12-x) = (0.7)12

Solving the above eqtn., my answer was x = 6

It would be helpful if someone can explain.

Thanks
Pavithra

You might have made some calculation error b/c I don't get 6 with the above statement.

.6x + 9.84 - .82x = 8.4

-.22x = -1.44

x = 144/22 = 72/11

Thanks... I did make a calculation mistake.

Pavithra