Question

A store sells small notebooks for ​$7 and large notebooks for ​$14. If a student buys 6 notebooks and spends ​$70, how many of each size did he​ buy?

Answer 1

4 large notebooks

2 small note books

Answer 2

Answer:

The student brought 2 small notebooks and 4 large notebooks.

Step-by-step explanation:

A store sells small notebooks for ​$7 and large notebooks for ​$14. If a student buys 6 notebooks and spends ​$70, how many of each size did he​ buy?

Let x be the number of small notebooks and y be the number of large notebooks. First write two equations in terms of x and​ y, one that models the amount of money spent and one that models the total number of notebooks that were bought.

Start by writing an equation that models the amount of money spent. Recall that each small notebook cost ​$7. ​Thus, if the student bought x small​ notebooks, what is the total cost of small notebooks in terms of​ x?

$7x

​Similarly, if he bought y large notebooks for ​$14 each, what is the total cost of large notebooks in terms of​ y?

$14y

Note that the total amount of money spent to buy the 6 notebooks is the total cost of small notebooks added to the total cost of large notebooks.​ Thus, use the information given in the problem statement to write a corresponding equation that models the situation.

7x+14y=70

Next write an equation that models the total number of​ notebooks, 6. Recall that the student bought x small notebooks and y large notebooks.

y+x=6

​Now, in order to use the table to solve for x and​ y, rewrite each equation in​ slope-intercept form and simplify.

I attached a picture to show what its supposed to look like. (Picture #1)

Now use a table to list possible​ x-values until the corresponding​ y-values match. Note that the total number of notebooks is 6.​ Thus, the possible values for the number of small​ notebooks, x, are​ 0, 1,​ 2, ..., 6. Start with the first 4 possible values of x. Calculate the number of large​ notebooks, y, in each​ equation, by substituting the corresponding value of x.

You need to create a table. I attached the table. (Picture #2)

Notice​ that, for the case where x is 2​, the value of y is 4 in both equations.​ Thus, the​ y-values match and there is no need to continue finding values.  

​Therefore, the student bought 2 small notebooks and 4 large notebooks.

So the student brought 2 small notebooks and 4 large notebooks.