Number of days ate 3? You begin with 28 sweets. Each day, you consume 2 or 3 sweets. In 12 days, you finish all 28.

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savs77

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Question: You begin with 28 sweets. Each day, you consume 2 or 3 sweets, and you finish all 28 sweets you started with on 12 separate days. How many times did you opt to eat 3 sweets?

I'm thinking.. if we say x is for the number of days I had 2 sweets, and y for the number of days where I had 3 sweets we would have this equation 2x + 3y = 28 is for all the sweets eaten. But then, considering the total days, x + y = 12. Does this seem right?
 
savs77 said:
Question: You begin with 28 sweets. Each day, you consume 2 or 3 sweets, and you finish all 28 sweets you started with on 12 separate days. How many times did you opt to eat 3 sweets?

I'm thinking.. if we say x is for the number of days I had 2 sweets, and y for the number of days where I had 3 sweets we would have this equation 2x + 3y = 28 is for all the sweets eaten. But then, considering the total days, x + y = 12. Does this seem right?
Click to expand...

If you ate only two each day, how many would you have eaten over the course of the twelve days?

How many sweets would be left over?

So how many days must you have eaten a third sweet?
 
savs77 said:
Question: You begin with 28 sweets. Each day, you consume 2 or 3 sweets, and you finish all 28 sweets you started with on 12 separate days. How many times did you opt to eat 3 sweets?

I'm thinking.. if we say x is for the number of days I had 2 sweets, and y for the number of days where I had 3 sweets we would have this equation 2x + 3y = 28 is for all the sweets eaten. But then, considering the total days, x + y = 12. Does this seem right?
Click to expand...
Yes!
You have been given a logical thought approach to solving your problem quite simply (above) but your own (Mathematical) approach to it is perfectly correct too.

You have set up a system of equations in which there are two unknowns and two equations relating them, therefore, you can go ahead and solve these equations simultaneously (which is what I suspect you were thinking of doing?) to find the values of both y and x (the number of days on which, as you defined them, you ate 3 and 2 sweets respectively).

You set up your equations as follows...

       Eq1.png​

If you multiply Equation (2) by 2 you then get Equation (3)...

Eq2.png​

And now subtracting Equation (3) from Equation (1), what do you get?

Hope that helps. 😊
 
stapel said:
If you ate only two each day, how many would you have eaten over the course of the twelve days?

How many sweets would be left over?

So how many days must you have eaten a third sweet?
Click to expand...
If you eat 2 on each of the 12 days, make 24, with 4 left over. You spread those 4 over different days, making 4 days on which 3 are eaten.
 
Last edited:
The Highlander said:
Yes!
You have been given a logical thought approach to solving your problem quite simply (above) but your own (Mathematical) approach to it is perfectly correct too.

You have set up a system of equations in which there are two unknowns and two equations relating them, therefore, you can go ahead and solve these equations simultaneously (which is what I suspect you were thinking of doing?) to find the values of both y and x (the number of days on which, as you defined them, you ate 3 and 2 sweets respectively).

You set up your equations as follows...

       View attachment 37512​

If you multiply Equation (2) by 2 you then get Equation (3)...


And now subtracting Equation (3) from Equation (1), what do you get?

Hope that helps. 😊
Click to expand...
Yes, I was thinking of solving them simultaneously. Subtracting 2x+2y=24 from 2x+3y=28 gives y=4. So I ate 3 sweets on four of the days.
 
@savs77

If you "like" what I've done for you, please come back and post your work showing a complete solution.

(A picture of your working (handwritten clearly & legibly, please) will suffice.) 👍😉

Thank you 😊
 
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