Question

i can solve real world problems and equations of the form $px+q=r$ and $p(x+q)=r$

1. during a film festival, the first film ticket is priced at $16, and each additional ticket is $11. if rico spends $71, then how many film tickets did he purchase?

equation: _______________
solution: _______________

1. five sisters each bought matching scarves and two pairs of socks. the scarves were priced at $12.00. if the total bill for all 5 sisters was $125.00, what was the price of one pair of socks?

equation: _______________
solution: _______________

1. ashers sister is eight years older than asher. their combined ages add up to 20. how old is asher?

equation: _______________
solution: _______________

1. on halloween night, mack collects x pieces of candy and then eats 7 pieces. the next day he eats 10% of his candy pieces and has 83 pieces remaining. how many pieces of candy did he collect on halloween night?

equation: _______________
solution: _______________

Explanation:

Problem 27

Step1: Define variable, set equation

Let $x$ = total tickets.
Equation: $16 + 11(x-1) = 71$

Step2: Simplify the equation

$16 + 11x - 11 = 71$
$11x + 5 = 71$

Step3: Isolate $11x$

$11x = 71 - 5$
$11x = 66$

Step4: Solve for $x$

$x = \frac{66}{11} = 6$

Problem 28

Step1: Define variable, set equation

Let $x$ = price of 1 sock pair.
Equation: $5(12 + 2x) = 125$

Step2: Divide both sides by 5

$12 + 2x = \frac{125}{5} = 25$

Step3: Isolate $2x$

$2x = 25 - 12$
$2x = 13$

Step4: Solve for $x$

$x = \frac{13}{2} = 6.5$

Problem 29

Step1: Define variable, set equation

Let $x$ = Asher's age.
Equation: $x + (x+8) = 20$

Step2: Simplify left side

$2x + 8 = 20$

Step3: Isolate $2x$

$2x = 20 - 8$
$2x = 12$

Step4: Solve for $x$

$x = \frac{12}{2} = 6$

Problem 30

Step1: Define variable, set equation

Let $x$ = initial candy pieces.
Equation: $0.9(x - 7) = 83$

Step2: Divide both sides by 0.9

$x - 7 = \frac{83}{0.9} = \frac{830}{9} \approx 92.22$

Step3: Solve for $x$

$x = \frac{830}{9} + 7 = \frac{830 + 63}{9} = \frac{893}{9} \approx 99.22$
(Note: For whole number context, adjust to exact fraction)

Answer:

1. Equation: $\boldsymbol{16 + 11(x-1) = 71}$; Solution: $\boldsymbol{6}$ tickets
2. Equation: $\boldsymbol{5(12 + 2x) = 125}$; Solution: $\boldsymbol{\$6.50}$ per pair
3. Equation: $\boldsymbol{x + (x+8) = 20}$; Solution: Asher is $\boldsymbol{6}$ years old
4. Equation: $\boldsymbol{0.9(x - 7) = 83}$; Solution: $\boldsymbol{\frac{893}{9} \approx 99}$ pieces