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Usimov [2.4K]
3 years ago
14

Hannah was saving for a new snowboard. the one she wanted originally cost $ 109. it had been marked down 10% and then another 12

%. a tax of 6% was added to final sale price. if Hannah had $90, did she have enough to buy the snowboard? Explain your answer.
Mathematics
2 answers:
Zigmanuir [339]3 years ago
6 0
First you would find the 10% discount of $109, which is equal to 90% of $109 or .9*$109 = $98.10.

You would then take $98.10 and find the 12% discount with is equal to 88% of $98.10 or .88*$98.10 = $86.33

Then you would add a 6% sales tax would would be 106% of $86.33 or 1.06*$86.33 = $91.51

Thus, she did not have enough to buy, and was $1.51 short. 
Semenov [28]3 years ago
3 0
So marked down 10 then 12 so 10+12=22
mark down total is 22%
100-22=78
78% of 109=0.78 times 109=85.02
tax of 6%
6+100=106%

85.02 times 1.06=90.1212 or about 90.12
90<90.12
no she is short 12 cents
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<h3>Answer: Choice D)  31.2 miles</h3>

This value is approximate.

============================================================

Explanation:

Let's focus on the 48 degree angle. This angle combines with angle ABC to form a 90 degree angle. This means angle ABC is 90-48 = 42 degrees. Or in short we can say angle B = 42 when focusing on triangle ABC.

Now let's move to the 17 degree angle. Add on the 90 degree angle and we can see that angle CAB, aka angle A, is 17+90 = 107 degrees.

Based on those two interior angles, angle C must be...

A+B+C = 180

107+42+C = 180

149+C = 180

C = 180-149

C = 31

----------------

To sum things up so far, we have these known properties of triangle ABC

  • angle A = 107 degrees
  • side c = side AB = 24 miles
  • angle B = 42 degrees
  • angle C = 31 degrees

Let's use the law of sines to find side b, which is opposite angle B. This will find the length of side AC (which is the distance from the storm to station A).

b/sin(B) = c/sin(C)

b/sin(42) = 24/sin(31)

b = sin(42)*24/sin(31)

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b = 31.2 miles is the distance from the storm to station A

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