20 Pts! Claire wrote down the number of centimeters that each plant in her science experiment grew last week as shown. 3, 4, 6,
3, 3, 5, 4, 2, 0, 1, 4, 3, 5, 3, 6, 4, 2, 2, 5, 1. Which line plot could Claire use to correctly show the data?
1 answer:
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Part (a)
- x = number of bass caught
- y = number of trout caught
x and y are nonnegative whole numbers.
3x represents the total weight of all the bass, since one bass weighs 3 pounds. Similarly, 2y is the total weight of the trout with each one being 2 pounds. Adding up all the weight of all the fish, we get 3x+2y. This is set equal to 34 pounds which is the total stated weight caught.
In short, we end up with the equation 3x+2y = 34
Now onto the second equation. The expression 5x represents how many points Pat gets from catching x bass, because he gets 5 points per bass. Then we subtract off 2y to represent Pat losing 2 points per trout he catches. Overall, his point total is 5x-2y. This is set equal to his point total of 14.
The second equation is 5x-2y = 14
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Answer:
3x+2y = 34
5x-2y = 14
Both equations are needed to form this particular system.
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Part (b)
We could use a number of methods to solve for (x,y). Possibly the most efficient is elimination. Why? Because note how we have 2y up top and -2y down below. They add to 0y which is just 0. The y terms go away, and are eliminated. Afterward, all we're left with is x in which we can solve for just like any other single variable equation. More info is in part (c).
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Part (c)
Refer to the answer in part (a). We'll add straight down. So that means we have these three sets of addition operations.
- 3x+5x becomes 8x
- 2y + (-2y), aka 2y-2y, becomes 0y and the y terms go away
- 34+14 simplifies to 48
After those three sets of addition operations, we're left with the much simpler equation 8x = 48. To solve this, we divide both sides by 8 and we get x = 6. This says Pat caught 6 bass.
Use this value of x to find y. So we'll plug x = 6 into either equation involving x,y and solve for y
3x+2y = 34
3(6)+2y = 34
18+2y = 34
2y = 34-18
2y = 16
y = 16/2
y = 8
So we can see that Pat caught 8 trout as well.
The check portion is shown in the attached image below. Effectively, all we're doing is replacing x and y with 6 and 8 respectively. Then we're simplifying both sides. Getting the same number on both sides results in a true equation, and therefore verifies we have the correct (x,y) solution.
Solution: (x,y) = (6,8)
Interpretation: Pat caught 6 bass and 8 trout
