A candy store sells malted milk balls for $2.50 per pound, and chocolate-covered raisins for $3.75 per pound. How many pounds of each should be used to make a 10 pound mixture that sells for $3.00 per pound?

Question

A candy store sells malted milk balls for $2.50 per pound, and chocolate-covered raisins for $3.75 per pound.  How many pounds of each should be used to make a 10 pound mixture that sells for $3.00 per pound?

anonymous · Answer

Set up two equations. One finds out "how much stuff", and one finds out "the cost".
x is milk balls, y is raisins.
x+y=10 lbs
2.50x+3.75y=3.00

anonymous · Answer

we have 2.5x+3.75y=30 
x + y = 10
solve the system we have x=6 y = 4
6 pounds of malted milk balls
and 4 pounds of covered raisins.
Yum!

anonymous · Answer

Now use the substitution method. Set the first equation equal to y (or x).
x=10-y
plug in 10-y wherever u see an x in the second equation
2.50(10-y)+3.75y=3.00

anonymous · Answer

Distribute the 2.50 and solve for y.
25-10y+3.75y=3.00
25-6.25y=3.00
-6.25y=-22
y=3.52

anonymous · Answer

hey gandalf, your setup of the second equation has a mistake

anonymous · Answer

:(

anonymous · Answer

it's 2.5x+3.75y=30

anonymous · Answer

because it's a ten-pound mixture and costs 3.00 per pound, and thus the total cost is going to be 30?

anonymous · Answer

OHHHH- missed that! Thank u! So, do the same steps except make 3 30.

anonymous · Answer

i got confused

anonymous · Answer

u want me 2 walk u through it lil?

anonymous · Answer

please, i got lost with the 3.30

anonymous · Answer

where did that come from?

anonymous · Answer

The candy-person wanted a 10 pound mixture costing 3 dollars per pound. Because there are ten pounds total, that means that the whole thing will cost 30 dollars. I had made a mistake and thought that the whole thing would only cost 3 dollars. 
I had meant in my former comment, if that's what confused you, that where I wrote 3.00, u should put down 30.00- sorry if I wrote it weird

anonymous · Answer

oh, ok

gw2011 · Answer

Let M = Malted Milk
Let C = Chocolate

2.50M + 3.75C = 30
M + C = 10 Solve for both equations by multiplying the second by 2.50

2.50M + 3.75C = 30
2.50M + 2.50C = 25 Subtract this equation from the first one

1.25C = 5
C = 4 Substitute this value into one of the equations to find M:

M + C = 10
M + 4 = 10
M = 6

You need 4 pounds of Chocolate and 6 pounds of Malted Milk