Gary is a fitness trainer who makes 30 and 45 minute appointments

with clients. Gary’s contract allows him to make up to 30 hours of

appointments in a week. State the inequality that represents all the

possible combinations of appointments that Gary can make in a

week. Graph the inequality.

3 years ago

Answered By Manasa R

You should start off by modelling this question. First start off with saying how many 30 minute appointments he can make and how many 45 minute appointments he can make. See where you can go from there.

3 years ago

Answered By Majid B

$x=$x= Number of 30-minutes $\left(\frac{1}{2}hour\right)$(12hour) appointments

$y=$y= Number of 45-minutes $\left(\frac{3}{4}hour\right)$(34hour) appointments

Let x be the number of 30 minute appointments (0.5x) Let y be the number of 45 minute appointments (0.75y) By adding these together you get an inequality that shows you the possible combinations that Gary can make in a week. Thus the equation becomes: 0.5x + 0.75y ≤ 30 (in hours)

For an equation in minutes, you multiply each value used by 60 and thus the equation becomes: 30x + 45y ≤ 1800

3 years ago

## Answered By Manasa R

You should start off by modelling this question. First start off with saying how many 30 minute appointments he can make and how many 45 minute appointments he can make. See where you can go from there.

3 years ago

## Answered By Majid B

$x=$x= Number of 30-minutes $\left(\frac{1}{2}hour\right)$(12 hour) appointments

$y=$y= Number of 45-minutes $\left(\frac{3}{4}hour\right)$(34 hour) appointments

$\left(\frac{1}{2}\right)x+\left(\frac{3}{4}\right)y\le30$(12 )x+(34 )y≤30

## Attached Graph:

3 years ago

## Answered By Palveen B

Let x be the number of 30 minute appointments (0.5x) Let y be the number of 45 minute appointments (0.75y) By adding these together you get an inequality that shows you the possible combinations that Gary can make in a week. Thus the equation becomes: 0.5x + 0.75y ≤ 30 (in hours)

For an equation in minutes, you multiply each value used by 60 and thus the equation becomes: 30x + 45y ≤ 1800

3 years ago

## Answered By Majid B

Restrictions:

$0\le x\le60$0≤x≤60

$0\le y\le40$0≤y≤40

3 years ago

## Answered By Grace T

30x+45y≤ 1800 (minutes)

0.5x+0.75y≤ 30 (hours)

3 years ago

## Answered By Swapan S

Combination 30 Mins 45 Mins 1 3 38 2 6 36 3 9 34 4 12 32 5 15 30 6 18 28 7 21 26 8 24 24 9 27 22 10 30 20 11 33 18 12 36 16 13 39 14 14 42 12 15 45 10 16 48 8 17 51 6 18 54 4 19 57 2 20 60 0## Attached Graph: