A 50-pound bag of feed is a mixture of two brands. Brand A costs $2.00 per pound and Brand B costs $1.00 per pound. The mixture is worth $1.34 per pound. How many pounds of each brand are in the mixture?

- anonymous

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- anonymous

you have to make the equations first

- amistre64

a+b = 50
a(2) + b(1) = 50(1.34)

- amistre64

b = 50 - a

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## More answers

- amistre64

2a + (50-a) = 50(1.34)
a + 50 = 50(1.34)
a = 50(1.34) - 50

- anonymous

a = 17
b = 33

- amistre64

a = 50(1.34-1)
a = 50(.34)

- amistre64

yep...a = 17
b = 50-17
b = 33..... yep :)

- amistre64

kecky; does that make sense?

- anonymous

yep i also got the same answer

- anonymous

yes

- amistre64

good :) youre a smart cookie :)

- anonymous

can you do this step by step

- amistre64

yes...

- anonymous

can you use x and y

- amistre64

what do we know?
we know that "a" and "b" equal 50 pounds:
a + b = 50
we should solve for one of these...
i choose "b"
You can use x and y if its easier for you; its just calling it a different name.

- amistre64

lets use x and y:
x + y = 50 ... now solve for "y" {or x, your choice}

- anonymous

y=-x+50

- amistre64

good:
now we also know that the 50 pounds bag costs 1.34 for "each pound".
we know that either x or y at this point have a price "for each pound"
right?

- anonymous

yes

- amistre64

lets apply that knowledge:
x(2.00) means whatever x is, the price will be 2 dollars for every "x" pounds...makes sense?
x(2) + y(1) = 50(1.34)
Does this make sense to you? and if not, let me know....

- anonymous

is it just like 2x+1y=50(1.34)

- anonymous

i think amistre is true...

- amistre64

that is exactly correct; now we substitute; or use the "value" we found for "y" in this equation to solve:
remember y=-x+50
can you plug that into the equation for me?

- amistre64

thanx tian :)

- anonymous

x y or a b is just a matter of notations, you're free to use what you want

- anonymous

yes 2x+1(-x+50)=1.34(50)

- amistre64

very good "ochin hoorah-show"!! :)
do you know how to solve for "x" with this equation now?

- anonymous

2x-1x+50=67

- amistre64

so far so good.... whats next?

- anonymous

put to the xs and take 50-67

- amistre64

lets try that "one step" at a time, so that we get it right and dont trip over anything ok? which one do you want to do first...doesnt matter, pick your favorite.

- anonymous

2-1=1

- amistre64

good; so 2x - 1x = 1x right?
we know have:
x + 50 = 67
whats next?

- anonymous

67-50=17
x=17

- amistre64

terrific!!
now that we know for sure the value of "x"; it equals 17.
we can figure out our first equation:
x + y = 50
How do we know what value y is now?

- anonymous

50-17=33
y=33

- amistre64

exactly.... good job :) does it make better sense now?
to double check our work;
we can use these x and y values in the other equation we came up with:
x(2) + y(1) = 50(1.34)
17(2) + 33(1) = 67
34 + 33 = 67
67 = 67 ... it checks out great :)

- anonymous

@amistre64 are you a teacher? you explained the solution very well

- anonymous

yes it does thank you!

- amistre64

dind; nah, just old and senile :)

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