At the post office, Amaya sorted 40 letters in 16 minutes. After a total of 32 minutes, she has sorted 80 letters. What coordinates would represent her work?
Let x represent the number of letters Amaya sorted in the first 16 minutes. We can set up an equation to represent this situation:
x/16 = 40.
Multiplying both sides of the equation by 16, we get:
x = 640.
Therefore, Amaya sorted 640 letters in the first 16 minutes.
Let y represent the number of additional letters Amaya sorted in the next 16 minutes. We can set up another equation to represent this situation:
y/16 = 80 - 40.
Simplifying, we get:
y/16 = 40.
Multiplying both sides of the equation by 16, we get:
y = 640.
Therefore, Amaya sorted an additional 640 letters in the next 16 minutes.
Since Amaya sorted 640 letters in the first 16 minutes and an additional 640 letters in the next 16 minutes, she sorted a total of 640 + 640 = 1280 letters in 32 minutes.
To represent her work, we can use the coordinates (32, 1280).
To represent Amaya's work, we can use a coordinate system with time (minutes) on the x-axis and number of letters sorted on the y-axis.
Given that Amaya sorted 40 letters in 16 minutes, we can plot the point (16, 40) on the coordinate system.
To find the coordinates after a total of 32 minutes, where she has sorted 80 letters, we can use a proportional relationship.
Since she sorted 40 letters in 16 minutes, we can set up the following proportion:
40 letters / 16 minutes = 80 letters / x minutes
Cross-multiplying, we get:
40x = 80 * 16
40x = 1280
x = 1280 / 40
x = 32
Therefore, after a total of 32 minutes, her coordinates would be (32, 80), representing that she sorted 80 letters.
To find the coordinates that would represent Amaya's work, we need to use the concept of rate. Let's break down the problem step by step:
1. Amaya sorted 40 letters in 16 minutes. This means her rate of work is 40 letters / 16 minutes = 2.5 letters/minute.
2. After a total of 32 minutes, she has sorted 80 letters. This tells us that her rate of work is still consistent because the number of letters sorted doubled while the time doubled. So, her rate remains 2.5 letters/minute.
Now, let's represent her work using coordinates. We'll use (x, y), where x represents the time in minutes and y represents the number of letters sorted.
At the beginning, she sorted 40 letters in 16 minutes: (16, 40).
After 32 minutes, she sorted 80 letters: (32, 80).
So, the coordinates that represent her work are (16, 40) and (32, 80).