Starting Algebra but this question has me so confused

bearynice

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A calculator and a pen were sold for x dollars. Jason bought 2 calculators and 4 pens for $16. How much did the 2 calculators cost altogether?
 

Dr.Peterson

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First, you need to understand that the answer will not be a number, but an expression in the variable x. Do you see that?

Now suppose you had been given a specific number in place of x:

A calculator and a pen were sold for 5 dollars. Jason bought 2 calculators and 4 pens for $16.​
How much did the 2 calculators cost altogether?​

Can you see any way to solve this problem (without using algebra)?

One way is to think about what it would cost to buy 4 calculators and 4 pens.

If you still have not idea what to do, it will be very helpful if you can tell us how much algebra you have learned. This is an odd problem, because x is not defined as a single quantity as we normally would; have you been given any examples similar to it? I'd like to see one (with its answer), to see what you are expected to do. It's possible that my idea may not be what they have in mind!
 

Jomo

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Can you please follow our guidelines and show us what you tried? Even if you know your work is wrong it will still help us help you.
 

bearynice

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sorry re guidelines! (mother posting on behalf of daughter here)... this is literally her first attempt at Algebra and I have no idea how to help her. The question did seem unusual to me. But here are her workings..
 

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Subhotosh Khan

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A calculator and a pen were sold for x dollars. Jason bought 2 calculators and 4 pens for $16. How much did the 2 calculators cost altogether?
According to response #4, your daughter has solved the problem correctly.
 

Dr.Peterson

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The answer, 2c = 4x-16, is correct, though I can't be sure of the thinking that arrived at it.

I would not normally expect a beginner to be using three variables (c, p, x), but in fact that is perhaps the easiest way. What I would have done here is to multiply the first equation by 4: 4c + 4p = 4x, and subtract the second equation from that: (4c + 4p) - (2c + 4p) = 4x - 16, and the left-hand side reduces to 2c.

I was expecting the same thing but without the variables: if one of each costs a total of x dollars, then 4 of each costs 4 x; 2 calculators and 4 pens is $16, and the difference is the cost of the extra two calculators. Using letters instead of words amounts to the same thing, but easier to say!
 
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