## Claire4christ 3 years ago somebody please help me with this question. Mr. Thompson has been asked to add storage space to a garage. He estimates 6 square feet per individual will be required to meet the needs of 12 people. If the storage space is 15% of the total amount of space required, how much total space does Mr. Thompson have? Mr. Thompson had______ square feet.

1. tcarroll010

A good start is to see how much total storage space is required. So, that part is given by 6 square feet for each person and there are 12 people.

2. Claire4christ

6x12=72

3. tcarroll010

Good. Now that you have that number. The initial number that you are starting with is only 15% of that.

4. Claire4christ

72x0.15

5. Claire4christ

480

6. Claire4christ

72/0.15=480

7. tcarroll010

Yes, and you are answering your own questions beautifully, which is the goal. Except that you have to multiply out 72 by 0.15 to get 10.8. So, yes to your first of the 3 answers above.

8. Claire4christ

An alloy weighing 30 lbs. is 11% tin. The alloy was made by mixing a 15% tin alloy and a 9% tin alloy. How many pounds of each alloy were used to make the 11% alloy? ___ lbs. of the 15% alloy and ___ lbs. of the 9% alloy.

9. tcarroll010

The 15% is basically saying that he needs 72, but he only has 15% of that to start with, so by eyeballing the 72 x 0.15, we know that it will be a fairly small number. For checking.

10. Claire4christ

can you help me with this one i dont get it

11. tcarroll010

This one is a little harder, but I can definitely help you.

12. tcarroll010

A lot of problems like this are made easier by first correctly conceptualizing the problem, and then the math is actually the easier part. We start by asking how much tin is actually in the 30 lbs. In 30 lbs., we have 0.11 of it as tin, so we have 30 x 0.11 lbs. or 3.3 lbs. Believe it or not, that's half the problem done.

13. Claire4christ

ok

14. Claire4christ

30x0.15=4.5

15. Claire4christ

i got 3.3 first answer and second one i got 7.2

16. tcarroll010

Now, let's call the 15% alloy as x lbs. and the 9% alloy as y lbs. The total weight we know from the problem is 30 lbs. So, we know that x + y = 30 because that is the total weight. We also know that (x)(0.15) + (y)(0.09) = 3.3 because we know we have 3.3 lbs. of tin total. So, we have 2 equations in 2 unknowns.

17. Claire4christ

can you put the in one equation little confused

18. Claire4christ

ok what is next i got this one

19. Claire4christ

now we have to solve for x right???

20. tcarroll010

So, are you ok with the 2 equations in the 2 unknowns, or are you stuck at this point?

21. Claire4christ

i need to know this ______ lbs. of the 15% alloy and ___ lbs. of the 9% alloy.

22. Claire4christ

there is a third part to this right??? solve for x

23. Claire4christ

3.3 is the first ansnwer right.

24. tcarroll010

Yes, that's from the problem statement. You have x + y = 30 and you have (0.15)x + (0.09)y = 3.3 These are your 2 equations for going forward with the problem. What I am asking is if you understand the derivation of the equations and the steps up to this point. Plus, a second question is are you able to solve simultaneous equations. I asked 2 questions. What are your 2 answers?

25. Claire4christ

y=35

26. tcarroll010

I'm looking for 2 yes/no answers at this point. Then we can proceed.

27. Claire4christ

i dont know what you looking for sorry

28. tcarroll010

29. Claire4christ

yes i do understand

30. tcarroll010

So, then all that is left is to solve the simultaneous equations for x and y, and from your last answer, you indicate that you are able to do that.

31. Claire4christ

x=21.4

32. Claire4christ

y=35

33. Claire4christ

x=3.21 y=3.15

34. tcarroll010

Your 2 simultaneous equations are x + y = 30 and (0.15)x + (0.09)y = 3.3. Solving the first equation for x, we have x = 30 - y. We substitute that into the second equation and solve for y. Y=20. We go back to the first equation with that y and find that x=10. So, 10 lbs. of the 15% alloy and 20 lbs. of the 9% alloy. And that's your answer.

35. Claire4christ

will you tell me how you got that

36. tcarroll010

(0.15)x + (0.09)y = 3.3 -> (0.15)(30-y) + (0.09)y = 3.3. And solve for y. This is a little bit more detail flowing from my previous post.

37. tcarroll010

(0.15)(30-y) + (0.09)y = 3.3 -> 4.5 - (0.15)y + (0.09)y = 3.3. Combine y's.