a store sells small notebooks for $8 and large notebooks for $10. If you buy 6 notebooks and spend $56, how many of each size notebooks did you buy?

Question

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Answer 1

Let s = #small notebooks

Let L = #large notebooks

 

We Can set up two equations from the info given.

 

s + L = 6           bought 6 notebooks total

8s + 10L = 56    spent $56

 

Solve equation 1 for one variable.

L = 6-s

 

Plug 6-s in equation 2 in place of L

and solve for s

 

8s + 10(6-s) = 56

8s + 60 - 10s = 56

-2s + 60 = 56

-2s = -4

s = (-4)/(-2)

s = 2

 

We know s+L = 6 and s=2

2+L = 6

L = 4

 

4 large notebooks and 2 small notebooks

were purchased

Answer 2

The best thing to do in these kind of questions is to try to write equations from the information given:

 

First of all we know you bought 6 notebooks. So one equation is

 

small+large=6

 

Also, we know that the total spent was $56 and we know the cost of each notebook. So

 

small*8 + large*10=56

 

Now that we have two equations we can substitute. So let's find small in terms of large

 

small+large=6

small=6-large

 

OK now we can substitute into the other equaion

small*8 + large*10=56

(6-large)*8 + large*10=56

 

Now let's solve for large

 

48-8*large+large*10=56

48+2*large = 56

2*large = 56-48

2*large = 8

large = 4

 

 

We know large is 4 and we know small=6-large. So we can now find small

small=6-large

small=6-4

small = 2

 

So you bought 2 small notebooks and 4 large ones.