## britbrat4290 2 years ago A ceramics workshop makes wreaths, trees, and sleighs for sale at Christmas. A wreath takes 3 hours to prepare, 2 hours to paint, and 9 hours to fire. A tree takes 14 hours to prepare, 3 hours to paint, and 4 hours to fire. A sleigh takes 4 hours to prepare, 15 hours to paint, and 7 hours to fire. If the workshop has 116 hours for prep time, 64 hours for painting, and 110 hours for firing, How many of each can be made?

1. britbrat4290

A. 8 wreaths, 6 trees, 2 sleighs B. 6 wreaths, 2 trees, 8 sleighs C. 9 wreaths, 7 trees, 3 sleighs D. 2 wreaths, 8 trees, 6 sleighs

2. Coolsector

call number of wreaths w , trees t and sleighs s. now you have 3 equations with 3 unknowns: 3w + 14t + 4s = 116 2w +3t + 15s = 64 9w+4t+7s=110

3. britbrat4290

i thought u cant add unlike terms

4. Coolsector

each equation is for different "process"

5. britbrat4290

ya i have no clu w/ this one

6. Coolsector

do you know how to solve these equations ?

7. britbrat4290

no

8. Coolsector

another way is plugging the answers into the equations .. the answer that satisfies all 3 equations is the correct one

9. britbrat4290

ohh ok gimmie a min to figure it out .. sry this ones easy went right over my head

10. Coolsector

but solving them is better since you wont always have answers. so lets do it using both elimination and substitution. if you multiply the first equation by 3 then subtract the 3rd one from the first you have: 38t+5s=238

11. Coolsector

ok. we can keep on solving it if you wish

12. britbrat4290

it would b a correct?

13. Coolsector

yes, A is the correct answer

14. britbrat4290

thanks!

15. Coolsector

but, it is really good practice to solve the equations by hand and not substituting answers

16. Coolsector

but, it's up to you :)

17. britbrat4290

its hard for me on the computer ... hence y im having some trouble in this class but im almost done thank god