Question

A sporting goods store has added a section with trail foods and snacks. Raisins cost $5.00 per pound and peanuts cost $3.80 per pound. Raisins and peanuts are going to be sold in a mixture of 30 pounds which will cost $4.05 per pound? How many pounds of raisins will be in the mix?

Answer 1

My education in math basically stopped at 6th grade. Could someone help me, please? I feel exremely stupid for not understanding what I am to do about this problem.

Answer 2

Dang, mixture problems. I'm in an 11th grade math course, we did this at the begginning of the year, and I've completely forgotten. I'm sure you're not the only one :)
Let me pull out my old books...

Answer 3

\[5x+3.80(30-x)=30\times 4.05\] solve for x

Answer 4

That is just numbers to me. Please take it step by step.

Answer 5

reason as follows
put x as the pounds of raisins
then since the total is 30 pounds, the number of pounds of peanuts must be 30- x

Answer 6

I multiply 30 by x? What is x?

Answer 7

you want 30 pounds of mixute that cost 4.05 per pound, so the total cost should be
\[4.05\times 30 = 112.50\]

Answer 8

hold on lets start again slowly

Answer 9

Okay.

Answer 10

you are looking for what? two numbers.
one is the number of pounds of raisins
the other is the number of pounds of peanuts

Answer 11

you don't know either of these two numbers, so you first need to name a variable, and the variable should be one of the two numbers.
i used x, you can use whatever you like
you should write down what your variable represents
i write
"let x be the number of pounds of raisins"

Answer 12

now i know that if we have "x" pounds of raisins we must have
\[30-x\] pounds of peanuts. why? because the total is 30
so for example if you have 5 pounds of raisins you would have 25 pounds of peanuts, and if you had 10 pounds of raising you would need 20 pounds of peanuts, and more generally if you have "x" pounds of raisins you must have
\[30-x\] pounds of peanuts

Answer 13

how are we doing so far?

Answer 14

?

Answer 15

So, I am to find what x is? So x is less than 30?

Answer 16

you wrote
"Raisins and peanuts are going to be sold in a mixture of 30 pounds..."

Answer 17

that means that the total is 30

Answer 18

Yes, but you wanted me to take x away from 30, so x is less than 30, no?

Answer 19

when i wrote
\[30-x\] is the number of pounds of peanuts, that is because the pounds of peanuts and the pounds of raisins have to add to 30

Answer 20

yes both numbers must be less than 30 because you will have 30 pounds total

Answer 21

Alright.

Answer 22

now rasins cost $5 a pound
if you have 2 pounds of raisins it will cost $10
if you have 4 pounds of raisins it will cost $20
if you have 7 pounds of raisins it will cost $35

more generally
if you have x pounds of raisins it will cost 5x dollars

Answer 23

Okay. I understand what you wrote.

Answer 24

likewise if you have
\[30-x\] pounds of peanuts, because they cost $3.80 a pound the total cost will be
\[3.80\times (30-x)\] for the peanuts

Answer 25

Right.

Answer 26

now we write down what the total cost will be two different ways. one was is easy
we have 30 pounds and the cost per pound is $4.05 (because you are told)

"30 pounds which will cost $4.05 per pound"

Answer 27

So I multiply $4.05 until I get $30?

Answer 28

so we multiply to get the total cost. it must be
\[4.05]\times 30 =\$121.50\]

Answer 29

no you multiply the cost per pound times the number of pounds

Answer 30

you know you have 30 pounds
you know it cost $4.05 per pound
so you know the total cost will be $121.50 by multiplication

Answer 31

so we actually know what the total cost is, it is number we can compute

Answer 32

What do they want me to find? The amount (money-wise) it takes for raisins to get to 30 lbs.?

Answer 33

on the other hand, we have an expression for the cost of the raisins. that expression is
\[5x\] and we also have an expression for the total cost of the peanuts,
that expression is
\[3.80(30-x)\] so another expression for the total of both is what you get when you add them up namely
\[5x+3.80(30-x)\]

Answer 34

no go back and make sure you remember what the problem is asking for
"how many pounds..."

Answer 35

This is much too complicated for me, I'm sorry.

Answer 36

so we have two expressions for the total cost, one is
\[5x+3.80(30-x)\] the other is 121.50 so write
\[5x+3.08(30-x)=121.50\] and solve for x

Answer 37

Like I said, I stopped progressing in math at 6th grade. I'm technically in 11th grade now.

Answer 38

ok well all the steps are there, that is i wrote them all down. if you have time see if you can understand what the steps entail and why they work the way they do
on the other hand if you cannot solve the above equation we are truly stuck.

good luck

Answer 39

I'm sorry for wasting your time. I'm a dead end when it comes to math :(