Two employees are wrapping gifts at the mall. sally has wrapped seven gifts already and is wrapping at a rate of two gift every half hour. john has wrapped 10 gifts and is wrapping at a rate of one gift every half hour. how long will it take for them to wrap the same number of gifts?

It will take them 1.5 hours to wrap the same number of gifts.

Step-by-step explanation:

1. The first thing that we should do is set up two equations to represent the number of gifts that they wrap.

a) Sally: y = 2x + 7

b) John: y = x + 10

Here, y represents the total number of gifts wrapped and x is the number of half hours that pass.

So, what we are saying is that:

a) for every half hour that passes, Sally wraps two gifts, and then she also has 7 gifts that she has already wrapped so we add that on.

b) for every half hour that passes, John wraps one gift, and then he also has 10 gifts that he has already wrapped so we add that on.

2. Now that we have our two equations, we need to find when the number of gifts they have wrapped is equal, ie. when the two equations are equal. Thus, when:

2x + 7 = x + 10

x + 7 = 10 (Subtract x from each side)

x = 3 (Subtract 7 from each side)

Now, remember that x represents the number of half hours, so:

3 half hours = 3*0.5 hours = 1.5 hours

Therefor, it takes them 1.5 hours (or 1 hour and 30 minutes) to wrap the same number of gifts.

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3