Question

1. the average of your 3 quiz grades is 17 points. two of your quiz grades are 14 points and 19 points. find your score on the remaining quiz.
2. the cost c (in dollars) of making a cabinet n feet long is represented by c = 18n + 45. how long is a cabinet that costs $447?
3. at the movies, you order 3 boxes of popcorn and a bottle of water. the cost of a bottle of water is $1.75. your total cost is $9.25. find the cost of one box of popcorn.
4. you and your friend each purchase n video games. your video games cost $65 each, and your friends video games cost $56 each. the total cost for you and your friend is $363. find the number of video games you purchased.
5. the sum of the measures of the interior angles of the parallelogram is 360°. find the value of x.
6. you had $26 in your pocket. you purchased x pens for $3.50 each. you now have $8.50 in your pocket. write and solve an equation to find the number of pens you purchased.

Explanation:

13.

Step1: Set up the equation

We know that $C = 18n+45$ and $C = 417$. So, $18n + 45=417$.

Step2: Isolate the term with $n$

Subtract 45 from both sides: $18n=417 - 45$, so $18n=372$.

Step3: Solve for $n$

Divide both sides by 18: $n=\frac{372}{18}=\frac{62}{3}=20\frac{2}{3}$ feet.

Step1: Let the cost of one - box of popcorn be $x$.

The total cost equation is $3x + 1.75=9.25$.

Step2: Isolate the term with $x$

Subtract 1.75 from both sides: $3x=9.25 - 1.75$, so $3x = 7.5$.

Step3: Solve for $x$

Divide both sides by 3: $x=\frac{7.5}{3}=2.5$.

Step1: Set up the equation

You and your friend each buy $n$ video - games. The total cost equation is $65n+56n = 363$.

Step2: Combine like terms

$(65 + 56)n=363$, so $121n=363$.

Step3: Solve for $n$

Divide both sides by 121: $n=\frac{363}{121}=3$.

Answer:

$20\frac{2}{3}$ feet

14.