Alison is buying binders for school. Small binders cost $3 each, and large binders cost $5 each.

Question

If Alison needs to buy at least 12 binders and has no more than $45 to spend, what is the maximum number of large binders she can buy?

Answer 1

Hi Anastasia,

this is a system of equations.

I set x = small binders and y= large binders

so x +y can be equal or greater than 12

then I set the values

3x + 5 y has to be less than 45.

Then I defined x in terms of y and then substituted.

3(12-y) + 5y = 45

then solve.

I hope this helps

Answer 2

1. Lets create our formula for binders and money to spend.
2. Small Binders=B
3. Large Binders= L
4. Money to spend= M
5. 3*B+5*L=M.
6. We also need to create a formula for Total Binders
7. Total Binders= T
8. B+L=T
9. T=12
10. B+L=12
11. Take the Total Binders equation and solve for B. We are solving for B to get rid of the small binder variable since the question is asking about large binders
12. B+L=12
13. Subtract L from both sides
14. B=12-L
15. Now that we know B=12-L we can plug that into the equation from step one.
16. 3*B+5*L=M
17. 3 (12-L)+5*L=M
18. Carry over the 3 to eliminate the parentheses. 3*12= 36 and -3*L
19. 36-3L+5L=M
20. Combine the Ls
21. 36+2L=M
22. Now we can replace M (money to spend) for the known amount 45. Then, we can solve for L (large binders).
23. 36+2L=45
24. Subtract 36 from both sides
25. 2L= 9
26. Divide 9 by 2
27. L= 4.5
28. Since we cannot buy a half of a binder we round the number down to 4. We round down since rounding up would cause us to spend more than $45.

Answer- You can buy 4 large binders.

Check the work- If you bought 5 large binders and 7 small binders your total would be $46. If you bought 6 large binders and 6 small binders your total would be $48, and so on.