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drek231 [11]
3 years ago
11

A skier is trying to decide whether or not to buy a season ski pass. a daily pass is $75. A season ski pass is $350. The skier w

ould have to rent skis with either pass for $30 per day. HOw many days would the skier have to go skiing in order to make the season pass less expensive than the daily pass?
Mathematics
1 answer:
pishuonlain [190]3 years ago
6 0
Since the skier has to rent skis for 30 dollars per day with both passes, we can ignore it while solving the question.

A season pass is 350, while a daily pass is 75.

\frac{350}{75} = \frac{25\times 14}{25\times 3} = \frac{14}{3} = 4 \frac{2}{3}

So a seasonal pass is equivalent to having 4.6667 daily passes. And you can't buy 0.6667 of a pass.

So, if you went at least 5 days with a seasonal pass, then the seasonal pass would be less expensive than a daily pass.
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The answer is:      "  3(m − 2)  "  .

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  →  The "factorized version" of the binomial expression, " 3m − 6 " ,  is:

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                →   "  3(m − 2) " .

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Explanation:

To solve:

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<u>Note</u>:  We are given the expression:  " 3m − 6 " ;

and we are asked to "factorize" this expression.

Note that this expression is a "binomial expression" — which means there are two (2) terms — in this case:   "3m" and "6" .

Since only one (1) of these 2 (two) terms has a variable, and the remaining terms is a "constant" (non-zero integer), write these 2 (two) terms as:

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       →   that is:  "3"  ;  and:

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→  With the numbers:  "3 and 6" , we can factor out a "3" ;  

          →  {since:  " 6 ÷ 3 = 2 "} ;

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               " 3m − 6 " ;  

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           →   Take the second term:  "  6 " :

                    "  6 = 3 * (what value?) ;

                 → divide each of this equation by "3" ;

    to isolate the "missing value" on one side of the equation; & to solve for the "missing value" ; as follows:

        →           "  6 / 3 = [ 3 * (what value?) ] / 3  ;

                    →  to get:  " 2  =  "(the missing value)"  ;

    →   So;    "  6 = 3 * (what value?) ;

           →     " 6 = 3 * 2 " .  

           →   Take the second term:  "  6 " :

           →     " 6 = 3 * 2 " .

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So:    " 3m − 6 "  =  (3 * m) − (3 * 2) " .  

Factor out a "3" ;  as follows:

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    →  " 3m − 6 "  =  (3 * m) − (3 * 2) " ;

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Let us check our answer:

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Note the "distributive property of multiplication"  :

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        a(b + c) = ab +  ac ;  

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So:  Take our answer:  " 3(m − 2) " .

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" 3(m − 2)  = ?  (3*m)  −  (3*2)  " ??  ;

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Let us substitute "4" for "m" ;  in both sides of the equation;

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 We have:

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     →  " 3(m − 2)  = ?  (3*m)  −  (3*2)  " ??  ;

First let us rewrite this equation;  substitute "4" for "m" ; as follows:

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And calculate;  to see if each side of the equation is equal ; i.e. to see if the equation holds true; as follows:

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     →   "  6  = ?  (6)  " ??  ;

     →   "  6 = 6 " !  Yes!  The equation holds true!

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Hope this answer was helpful!

Best wishes!

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