You are choosing between two health clubs. Club A offers membership for a fee of $ 28$28 plus a monthly fee of $ 20.$20. Club B offers membership for a fee of $ 19$19 plus a monthly fee of $ 23.$23. After how many months will the total cost of each health club be the same? What will be the total cost for each club?

That is to say that at 3 months, the values of the club are equal.

Club A = 268 dollars in total

Club B = 295 dollars in total

Step-by-step explanation:

The first thing is to propose an equation for each club. Let m be the number of months.

Club A = 28 + 20 * m

Club B = 19 + 23 * m

Now, to know when it is the same, we must equal the value of Club A with Club B, it would look like this

28 + 20 * m = 19 + 23 * m

By rearranging the equation we have:

23 * m - 20 * m = 28-19

3 * m = 9

m = 3

That is to say that at 3 months, the values of the club are equal.

Now to know the total value, we will do it with an annual membership, which would be a total of 12 months, therefore it is to replace in the equation of each one:

Club A = 28 + 20 * 12 = 268 dollars in total

Club B = 19 + 23 * 12 = 295 dollars in total

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step-by-step explanation:

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: