Basic Word Problem

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mathinept

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A discount store sold plastic cups for $3.25 each and ceramic cups for $4.50 each.

a. If 500 cups were sold for a total of $2,090, how many cups of each type were sold?

What I've worked out so far
Answer: 3.25n = plastic cups
4.50n = ceramic cups

It's not much I know. I don't know how many more of one type of cups over the other was sold. I am lost how to figure this out.

I've done the division for 2090/500 = 4.18
and I've done the addition 3.25n + 4.50 n = 7.75 n

I don't know how to set it up

3.25n+7.75n (what about the 500? divide it? multiply it?) = 2090

if I divide it, I'd get 500/7.75 = 64.52

if I multiply it, I get 3875

how would I get either to compute down or up to 2090?

I just don't get this. Any help greatly appreciated.
 
i messed this part of my question up
3.25n+7.75n (what about the 500? divide it? multiply it?) = 2090

what i am trying to figure out is 7.75 (do what with it to get it to) 2090

divide, multiply? sorry I didn't notice i mixed that.
 
mathinept said:
A discount store sold plastic cups for $3.25 each and ceramic cups for $4.50 each.

a. If 500 cups were sold for a total of $2,090, how many cups of each type were sold?

First determine - what you need to find and name those as unknown variables. Here we need to find "# of plastic cup sold" & "# of ceramic cup sold". So, let

"# of plastic cup sold" = P

"# of ceramic cup sold" = C

We know: "If 500 cups were sold" - then

P + C = 500................................(1)

P = 500 - C ...............................(2)

Also we know: cups were sold for a total of $2,090, and plastic cups for $3.25 each and ceramic cups for $4.50 each

3.25 * P + 4.5 * C = 2090..............................................(3)

Using (2) in (3)

3.25 * (500 - C) + 4.5 * C = 2090

Solve for C from above - and use that in (2) to solve for P

Finally check your answer by putting these values in original equations (1) & (3)



What I've worked out so far
Answer: 3.25n = plastic cups
4.50n = ceramic cups

It's not much I know. I don't know how many more of one type of cups over the other was sold. I am lost how to figure this out.

I've done the division for 2090/500 = 4.18
and I've done the addition 3.25n + 4.50 n = 7.75 n

I don't know how to set it up

3.25n+7.75n (what about the 500? divide it? multiply it?) = 2090

if I divide it, I'd get 500/7.75 = 64.52

if I multiply it, I get 3875

how would I get either to compute down or up to 2090?

I just don't get this. Any help greatly appreciated.
Click to expand...
 
Thank you very much for your response!

so... here i go

i've got
3.25p = plastic
4.5 c = ceramic

(3.25p + 4.50c)500 = 2090

1625p + 2250c - 2250c = 2090

= 1625 p = 2090

p = 1.29

1625p - 1625p + 2250c = 2090
= 2250c = 2090
c = .93

3.25* 1.29 = 4.19

4.5* .93 = 4.12

(4.19 + 4.12)500 = 2090


2095 + 2060 eek doesn't = 2090

Where am I messing it up?
 
Follow my instructions - you'll not mess up!
 
mathinept said:
Thank you very much for your response!

so... here i go

i've got
3.25p = plastic <<<<<<<<<<What is this - plastic what? Money received from selling 1 plastic mug? What is "p"? Need to define your variables carefully
4.5 c = ceramic <<<<<<<<<<What is this - ceramic what? Money received from selling 1 ceramic mug? What is "c"? Need to define your variables carefully

(3.25p + 4.50c)500 = 2090 <<< How did you get this equation - from which statement

1625p + 2250c - 2250c = 2090

= 1625 p = 2090

p = 1.29

1625p - 1625p + 2250c = 2090
= 2250c = 2090
c = .93

3.25* 1.29 = 4.19

4.5* .93 = 4.12

(4.19 + 4.12)500 = 2090


2095 + 2060 eek doesn't = 2090

Where am I messing it up?
Click to expand...
 
Okay - I'll finish this problem.

Subhotosh Khan said:
mathinept said:
A discount store sold plastic cups for $3.25 each and ceramic cups for $4.50 each.

a. If 500 cups were sold for a total of $2,090, how many cups of each type were sold?

First determine - what you need to find and name those as unknown variables. Here we need to find "# of plastic cup sold" & "# of ceramic cup sold". So, let

"# of plastic cup sold" = P

"# of ceramic cup sold" = C

We know: "If 500 cups were sold" - then

P + C = 500................................(1)

P = 500 - C ...............................(2)

Also we know: cups were sold for a total of $2,090, and plastic cups for $3.25 each and ceramic cups for $4.50 each

3.25 * P + 4.5 * C = 2090..............................................(3)

Using (2) in (3)

3.25 * (500 - C) + 4.5 * C = 2090

1625 - 3.25 * C + 4.5 * C = 2090

1.25 * C = 2090 - 1625 = 465

C = 465/1.25 = 372

P = 500 - C = 500 - 372 = 128

check

3.25*P + 4.5*C

= 3.25*128 + 4.5*372

= 416 + 1674

= 2090

checks.....

.
Click to expand...
Click to expand...
 
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