Question

Ammon and Nika volunteer at an animal shelter, Nakia worked 3 more hours than Ammon. They each worked a whole number of hours. They together worked more than 27 hours. What is the least number of hours each worked?

Answer 1

both of they hours added is 27
and one of them worked 3 hrs more

Answer 2

x = # of hours Ammon worked
y = # of hours Nika worked


"Nakia worked 3 more hours than Ammon"

so y = x + 3 is your first equation

Answer 3

their*

Answer 4

" They together worked more than 27 hours"

so the sum of their hours, x+y, has to be more than 27

meaning that x+y > 27

Answer 5

x+y > 27

x+x+3 > 27 ... replace y with x+3 (works because y = x+3)

solve for x

Answer 6

\[is \it 5x >27\]

Answer 7

is it*

Answer 8

should be

2x+3 > 27

2x > 27-3

2x > 24

x > ???

Answer 9

12?

Answer 10

yep x > 12

Answer 11

ok ty

Answer 12

so recall that we said that "x = # of hours Ammon worked"

so x > 12 means Ammon worked more than 12 hrs

the min Ammon can work is therefore 13 hours (he worked a whole number of hours)

Answer 13

use x = 13 to find y

Answer 14

how

Answer 15

y = x+3 is the first equation we set up

Answer 16

plug in x = 13

Answer 17

thanks i got the answer

Answer 18

I have another problem

Answer 19

alright, I'll help with one more

Answer 20

thanks

Answer 21

its a word problem

Answer 22

The length of a rectangle is 4cm longer than the width, and the perimeter is at least 48 cm. What are the smallest possible dimensions of the rectangle?

Answer 23

"The length of a rectangle is 4cm longer than the width"

L = W+4

L is the length, W is the width

Answer 24

"perimeter is at least 48 cm"

P >= 48

2L+2W >= 48

2(W+4)+2W >= 48

solve for W

Answer 25

ok hold on

Answer 26

\[w \ge10\]

Answer 27

correct

Answer 28

now plug w = 10 into L = w+4

Answer 29

L=14

Answer 30

L = 14 is correct