Lincoln is preparing many gifts for a family holiday party. Each gift must either be wrapped with wrapping paper or prepared in a gift bag. Lincoln can wrap a single gift in 6.5 minutes and he can do a giftbag in 2 minutes. Lincoln prepared a total 13 gifts in 57.5 minutes. Write a system of equations that could be used to determine the number of gifts Lincoln wrapped and the number of giftbags he prepared. Define the variables that you use to write the system.
w = #wraps
b = #bags
w+b = 13
6.5w + 2b = 57.5
now work your magic.
Well, it looks like Lincoln has been quite busy with his gift preparations! Let's figure out the system of equations.
Let's define the variables:
Let's say the number of gifts Lincoln wrapped with wrapping paper is 'w'.
And let's say the number of gifts Lincoln prepared in gift bags is 'b'.
Now, let's write the system of equations based on the given information:
1. The time it took to wrap 'w' gifts with wrapping paper is 6.5 minutes per gift. So, the total time spent wrapping gifts is 6.5w minutes.
2. The time it took to prepare 'b' gifts in gift bags is 2 minutes per gift. So, the total time spent preparing gift bags is 2b minutes.
Equation 1: 6.5w + 2b = 57.5 (since the total time spent cannot exceed 57.5 minutes)
3. The total number of gifts Lincoln prepared is 13. So, the number of gifts wrapped with wrapping paper plus the number of gifts prepared in gift bags must equal 13.
Equation 2: w + b = 13
To summarize, the system of equations is:
6.5w + 2b = 57.5
w + b = 13
I hope this helps, and good luck to Lincoln with his gift preparations!
Let's define the variables:
Let's say the number of gifts Lincoln wrapped is x.
Let's say the number of gift bags Lincoln prepared is y.
Now let's write the equations based on the given information:
1. The time taken to wrap a single gift is 6.5 minutes, so the total time taken to wrap x gifts is 6.5x.
2. The time taken to prepare a gift bag is 2 minutes, so the total time taken to prepare y gift bags is 2y.
3. The total number of gifts prepared is 13.
4. The total time taken is 57.5 minutes.
So, the system of equations can be written as:
6.5x + 2y = 57.5 (equation 1)
x + y = 13 (equation 2)
These equations represent the number of gifts Lincoln wrapped and the number of gift bags he prepared.
Let's define:
x = the number of gifts wrapped with wrapping paper
y = the number of gifts prepared in a gift bag
We are told that Lincoln wrapped a single gift in 6.5 minutes, so the time spent wrapping x gifts would be 6.5x minutes.
We are also told that Lincoln can do a gift bag in 2 minutes, so the time spent preparing y gift bags would be 2y minutes.
Lincoln prepared a total of 13 gifts, so the total number of gifts wrapped and prepared in gift bags is 13.
The time spent wrapping and preparing the gifts is a total of 57.5 minutes.
Putting it all together, we can set up the following system of equations to represent the given information:
Equation 1: x + y = 13 (the total number of gifts wrapped and prepared in gift bags is 13)
Equation 2: 6.5x + 2y = 57.5 (the total time spent wrapping and preparing the gifts is 57.5 minutes)
These two equations can be used to determine the number of gifts Lincoln wrapped (x) and the number of gift bags he prepared (y).