Question

extremely confused. Algebra 2 Word problem.
At a local produce stand sugar-coated strawberries sell for $3 dollare per pund and chocolate covered bananas sell for $4 per ound. How many punds of strawberries must be purchased to have a 5-pound mixture that costs $3.60 per pound?

Answer 1

Set up a system of two linear equations: one for total weight, one for total cost.

Answer 2

e.g. You can use S=pounds of strawberries, and B=pounds of bananas, so
S+B=5

Answer 3

Can you get the second equation for total cost?

Answer 4

4b + 3s = 3.60 ?

Answer 5

Very close! The $3.60 is per pound. You need to multiply that by 5 pounds to get the total cost.

Answer 6

so 4b+3s=18 ?

Answer 7

That should do it.

Answer 8

yah im stuck I got to s = 5,75 - 5b/4

Answer 9

this looks like a good idea, but may be too much work
if you call the number of pounds of bananas say \(x\) then since the number of pounds total is 5 the number of pounds of strawberries is necessarily \(5-x\) since they have to add to 5
then the total cost will be
\[4x+3(5-x)\] and you want that to be \(3.6\times 5=18\) so solve
\[4x+3(5-x)=18\] for \(x\)

Answer 10

in other words take your first equations

S+B=5

solve for B

Answer 11

sub into the second equation

Answer 12

@satellite73 i got x= 3 now what

Answer 13

If the total weight is 5 pounds and you have 3 pounds of bananas . . .

Answer 14

so 2 pounds of strawberries? right

Answer 15

You can check it by putting those numbers back into your original equations to see if they both work.

Answer 16

that is why it is very very important to write as a first step what your variable represents
notice the first think i wrote was
"call the number of pounds of bananas say \(x"\)

Answer 17

that is so when you solve, you can go back and say "oh, what was \(x\) i forget?" and then look and see that \(x\) is a number, namely the number of pounds of bananas in this case
so you can be assured that you have 3 pounds of bananas (in this example)

Answer 18

if you are still there i hope i have convinced you that you should not skip this step, actually write down on paper "let \(x\) be the number of ..."

Answer 19

@satellite, that's why I recommended S=pounds of strawberries, and B=pounds of bananas; not only defines the variables, but they are easy to remember which is which.

Answer 20

yeah that is actually a better plan, isn't it? i am just so used to typing \(x\) that when i try with other variables i make lots of typos.

Answer 21

I know what you mean. Sometimes, good ol' x and y make everything familiar and easy to work with. ;-)