Problem 1
Answer: Choice A, Choice B, and choice C
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Explanation:
x = number of hats made,
12*x = total time to knit just hats (12 hrs to do 1 hat)
y = number of scarves made
6*y = total time to knit just scarves (6 hrs to do 1 scarf)
In total, it takes 12x+6y hours to knit everything (scarves+hats) and we want this total time to be 20 or less, so this means choice B is one of the answers
Choice A and choice C are also answers because they restrict how many scarves and hats we can make. Choice A says we can make at most 8 scarves. Choice C says the max number of hats we can make is 5.
The other inequalities won't apply so they can be crossed off the list.
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Problem 2
Answer: choice A and choice B
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Explanation:
If you plug in x = -2 and simplify, you'll end up with f(x) = -4, so that helps confirm A is one of the answers. Choice B is the other answer because x = 2 leads to f(x) = 56
In contrast, if you plugged in x = 8, you'd end up with 4088 which is way off of the y coordinate 0 listed. The same story happens with x = 24 but the result is much much larger.
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Problem 3
To be honest, I'm not sure what to make of this problem. If x is the decimal form of the sales tax, then 1+x would be the multiplier to help get the total cost. For example, if x = 0.02 then 1+x = 1+0.02 = 1.02, meaning that the final cost (after tax) is 102% of the original cost (before tax)
1+x isn't the amount of tax as that would be 15.85*x
The percent of tax would be 100*x (eg: x = 0.02 so 100*x = 100*0.02 = 2% tax rate)
The cost of the toy is given to be 15.85 so that answer is out as well.
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