Answer:
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.
