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Leona [35]
3 years ago
6

The cost of four scarfs and six hats is $52. The cost of two hats is $1 more than the cost of one scarf. What are the costs of o

ne scarf and one hat?
Mathematics
2 answers:
timurjin [86]3 years ago
8 0
Four scarves and six hats is $52.00 
<span>4s+6h=52 </span>

<span>two hats is $1.00 more than the cost of one scarf. </span>
<span>2h=1s+1 </span>
<span>2h=s+1 </span>
<span>s=2h-1 </span>

<span>substitute for s </span>
<span>4s+6h=52 </span>
<span>4(2h-1)+6h=52 </span>
<span>8h-4+6h=52 </span>
<span>14h=56 </span>
<span>h=4 </span>

<span>s=2h-1 </span>
<span>s=8-1 </span>
<span>s=7 </span>

<span>a scarf cost $7 </span>
<span>a hat cost $4</span>
WINSTONCH [101]3 years ago
7 0

Answer with Step-by-step explanation:

Let s represents the cost of scarfs

and h represents the cost of hats.

Cost of four scarfs and six hats is $52.00 

i.e. 4s+6h=52 

Cost of two hats is $1.00 more than the cost of one scarf. 

i.e. 2h=s+1 

s=2h-1 

substituting s in 4s+6h=52 

4(2h-1)+6h=52 

8h-4+6h=52 

14h=56 

h=4 

s=2h-1 

s=8-1 

s=7 

Hence,

Cost of one scarf= $7 

and Cost of one hat= $4

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Complete proof is written below.

Facts and explanation about the segments shown in question :

  1. As BC = EF is a given statement in the question
  2. AB + BC = AC because the definition of betweenness gives us a clear idea that if a point B is between points A and C, then the length of AB and the length of BC is equal to the length of AC. Also according to Segment addition postulate, AB + BC = AC. For example, if AB = 5 and BC= 7 then AC = AB + BC → AC = 12
  3. AC > BC because the Parts Theorem (Segments) mentions that if B is a point on AC between A and C, then AC > BC and AC>AB. So, if we observe the question figure, we can realize that point B lies on the segment AC between points A and C.
  4. AC > EF because BC is equal to EF and if AC>BC, then it must be true that the length of AC must greater than the length segment EF.

Below is the complete proof of the observation given in the question:

<em />

<em>STATEMENT                              REASON  </em>

___________________________________________________

1. BC = EF                                    1. Given

2. AB + BC = AC                         2. Betweenness

3. AC > BC                                   3. Def. of segment inequality

4. AC > EF                                   4. Def. of congruent segments

<em />

<em>Keywords: statement, length, reason, proof</em>

<em> Learn more about proof from brainly.com/question/13005321</em>

<em> #learnwithBrainly</em>

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