Question

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?

Answer 1

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

Answer 2

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

Answer 3

i thought u cant add unlike terms

Answer 4

each equation is for different "process"

Answer 5

ya i have no clu w/ this one

Answer 6

do you know how to solve these equations ?

Answer 7

no

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

ok. we can keep on solving it if you wish

Answer 12

it would b a correct?

Answer 13

yes, A is the correct answer

Answer 14

thanks!

Answer 15

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

Answer 16

but, it's up to you :)

Answer 17

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