QuestionMalik has a \ $50 gift card for movies costing \$6 each. Write a sequence rule and find how many movies he can see.$ $f(x)=$ $ Malik can see movies to deplete the card.

Studdy Solution

STEP 1

Assumptions1. The initial value on the gift card is $50. The cost of each movie is$ 63. The value left on the card decreases by the cost of a movie each time Malik sees a movie4. Malik uses the gift card only for movie admissions

STEP 2

We can represent the value left on the card as an arithmetic sequence where the initial term (a) is the initial value on the gift card and the common difference (d) is the negative of the cost of each movie.
$f(x) = a + (x -1) \cdot d$

STEP 3

Now, plug in the given values for the initial value on the gift card (a = $50) and the cost of each movie (d = -$ 6) to write the arithmetic sequence rule.
$f(x) = \$50 + (x -1) \cdot -\$6$

STEP 4

implify the arithmetic sequence rule.
$f(x) = \$50 - \$6 \cdot (x -1)$

STEP 5

Now, to find out the number of movies Malik would have seen to deplete the gift card, we set the value left on the card (f(x)) to $0 and solve for x.
$0 = \$50 - \$ \cdot (x -1)$

STEP 6

olve the equation for x.
First, distribute the $-6$ to the terms inside the parentheses.
$0 = \$50 - \$6x + \$6$

STEP 7

Combine like terms.
$0 = \$56 - \$6x$

STEP 8

Rearrange the equation to isolate the term with x.
$\$6x = \$56$

STEP 9

Divide both sides of the equation by $6$ to solve for x.
$x = \$56 / \$6$

STEP 10

Calculate the value of x.
$x = \$56 / \$6 =9.33$ Since Malik can't see a fraction of a movie, we round this up to the nearest whole number. So, Malik would have seen10 movies to deplete the gift card.

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QuestionMalik has a \ $50 gift card for movies costing \$6 each. Write a sequence rule and find how many movies he can see.$ $f(x)=$ $ Malik can see movies to deplete the card.

Studdy Solution

STEP 1

Assumptions1. The initial value on the gift card is $50. The cost of each movie is$ 63. The value left on the card decreases by the cost of a movie each time Malik sees a movie4. Malik uses the gift card only for movie admissions

STEP 2

We can represent the value left on the card as an arithmetic sequence where the initial term (a) is the initial value on the gift card and the common difference (d) is the negative of the cost of each movie.
$f(x) = a + (x -1) \cdot d$

STEP 3

Now, plug in the given values for the initial value on the gift card (a = $50) and the cost of each movie (d = -$ 6) to write the arithmetic sequence rule.
$f(x) = \$50 + (x -1) \cdot -\$6$

STEP 4

implify the arithmetic sequence rule.
$f(x) = \$50 - \$6 \cdot (x -1)$

STEP 5

Now, to find out the number of movies Malik would have seen to deplete the gift card, we set the value left on the card (f(x)) to $0 and solve for x.
$0 = \$50 - \$ \cdot (x -1)$

STEP 6

olve the equation for x.
First, distribute the $-6$ to the terms inside the parentheses.
$0 = \$50 - \$6x + \$6$

STEP 7

Combine like terms.
$0 = \$56 - \$6x$

STEP 8

Rearrange the equation to isolate the term with x.
$\$6x = \$56$

STEP 9

Divide both sides of the equation by $6$ to solve for x.
$x = \$56 / \$6$

STEP 10

Calculate the value of x.
$x = \$56 / \$6 =9.33$ Since Malik can't see a fraction of a movie, we round this up to the nearest whole number. So, Malik would have seen10 movies to deplete the gift card.

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Studdy Solution

STEP 1

Assumptions1. The initial value on the gift card is 50.Thecostofeachmovieis50. The cost of each movie is 50.Thecostofeachmovieis63. The value left on the card decreases by the cost of a movie each time Malik sees a movie4. Malik uses the gift card only for movie admissions

STEP 2

We can represent the value left on the card as an arithmetic sequence where the initial term (a) is the initial value on the gift card and the common difference (d) is the negative of the cost of each movie.f(x)=a+(x−1)⋅df(x) = a + (x -1) \cdot df(x)=a+(x−1)⋅d

STEP 3

Now, plug in the given values for the initial value on the gift card (a = 50)andthecostofeachmovie(d=−50) and the cost of each movie (d = -50)andthecostofeachmovie(d=−6) to write the arithmetic sequence rule.f(x)=$50+(x−1)⋅−$6f(x) = \$50 + (x -1) \cdot -\$6f(x)=$50+(x−1)⋅−$6

STEP 4

implify the arithmetic sequence rule.f(x)=$50−$6⋅(x−1)f(x) = \$50 - \$6 \cdot (x -1)f(x)=$50−$6⋅(x−1)

STEP 5

Now, to find out the number of movies Malik would have seen to deplete the gift card, we set the value left on the card (f(x)) to $0 and solve for x.0=$50−$⋅(x−1)0 = \$50 - \$ \cdot (x -1)0=$50−$⋅(x−1)

STEP 6

olve the equation for x.First, distribute the −6-6−6 to the terms inside the parentheses.0=$50−$6x+$60 = \$50 - \$6x + \$60=$50−$6x+$6

STEP 7

Combine like terms.0=$56−$6x0 = \$56 - \$6x0=$56−$6x

STEP 8

Rearrange the equation to isolate the term with x.$6x=$56\$6x = \$56$6x=$56

STEP 9

Divide both sides of the equation by 666 to solve for x.x=$56/$6x = \$56 / \$6x=$56/$6

STEP 10

Calculate the value of x.x=$56/$6=9.33x = \$56 / \$6 =9.33x=$56/$6=9.33Since Malik can't see a fraction of a movie, we round this up to the nearest whole number. So, Malik would have seen10 movies to deplete the gift card.

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Assumptions1. The initial value on the gift card is $50. The cost of each movie is$ 63. The value left on the card decreases by the cost of a movie each time Malik sees a movie4. Malik uses the gift card only for movie admissions

We can represent the value left on the card as an arithmetic sequence where the initial term (a) is the initial value on the gift card and the common difference (d) is the negative of the cost of each movie.
$f(x) = a + (x -1) \cdot d$

Now, plug in the given values for the initial value on the gift card (a = $50) and the cost of each movie (d = -$ 6) to write the arithmetic sequence rule.
$f(x) = \$50 + (x -1) \cdot -\$6$

implify the arithmetic sequence rule.
$f(x) = \$50 - \$6 \cdot (x -1)$

Now, to find out the number of movies Malik would have seen to deplete the gift card, we set the value left on the card (f(x)) to $0 and solve for x.
$0 = \$50 - \$ \cdot (x -1)$

olve the equation for x.
First, distribute the $-6$ to the terms inside the parentheses.
$0 = \$50 - \$6x + \$6$

Combine like terms.
$0 = \$56 - \$6x$

Rearrange the equation to isolate the term with x.
$\$6x = \$56$

Divide both sides of the equation by $6$ to solve for x.
$x = \$56 / \$6$

Calculate the value of x.
$x = \$56 / \$6 =9.33$ Since Malik can't see a fraction of a movie, we round this up to the nearest whole number. So, Malik would have seen10 movies to deplete the gift card.