Question

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?

Answer 1

you have to make the equations first

Answer 2

a+b = 50

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

Answer 3

b = 50 - a

Answer 4

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

a + 50 = 50(1.34)

a = 50(1.34) - 50

Answer 5

a = 17
b = 33

Answer 6

a = 50(1.34-1)

a = 50(.34)

Answer 7

yep...a = 17

b = 50-17

b = 33..... yep :)

Answer 8

kecky; does that make sense?

Answer 9

yep i also got the same answer

Answer 10

yes

Answer 11

good :) youre a smart cookie :)

Answer 12

can you do this step by step

Answer 13

yes...

Answer 14

can you use x and y

Answer 15

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.

Answer 16

lets use x and y:

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

Answer 17

y=-x+50

Answer 18

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?

Answer 19

yes

Answer 20

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....

Answer 21

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

Answer 22

i think amistre is true...

Answer 23

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?

Answer 24

thanx tian :)

Answer 25

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

Answer 26

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

Answer 27

very good "ochin hoorah-show"!! :)

do you know how to solve for "x" with this equation now?

Answer 28

2x-1x+50=67

Answer 29

so far so good.... whats next?

Answer 30

put to the xs and take 50-67

Answer 31

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.

Answer 32

2-1=1

Answer 33

good; so 2x - 1x = 1x right?

we know have:

x + 50 = 67

whats next?

Answer 34

67-50=17
x=17

Answer 35

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?

Answer 36

50-17=33
y=33

Answer 37

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 :)

Answer 38

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

Answer 39

yes it does thank you!

Answer 40

dind; nah, just old and senile :)