Question

1. solve the equation.$2 + 5t - 3 = 34$a. 6.6 b. 7 c. 5.8 d. 66. solve the equation.$17 - 5m - 6m = 50$a. 3 b. -3 c. 33 d. -337. which equation represents the verbal sentence:twice a number plus 5 is equal to 27?a. $2n - 5 = 27$ b. $20n + 5 = 27$c. $2(n + 5) = 27$ d. $2n + 5 = 27$use the following information for 8 & 9.a taxi service charges an initial fee of $1.50 plus $1.50 for every mile traveled. a taxi ride costs $21.00. how many miles did the taxi travel?8. choose the correct variable.a. t = number of taxis b. r = number of ridersc. m = number of miles d. f = amount of fees9. choose the correct equation to answer the question.a. $3m = 21$ b. $1.5m = 21$c. $1.5m + 1.5 = 21$ d. $1.5m - 1.5 = 21$

Explanation:

Problem 5

Step1: Combine constant terms

$2 - 3 + 5t = 34$
$\implies -1 + 5t = 34$

Step2: Isolate the variable term

$5t = 34 + 1$
$\implies 5t = 35$

Step3: Solve for $t$

$t = \frac{35}{5}$
$\implies t = 7$

Problem 6

Step1: Combine like variable terms

$17 - (5m + 6m) = 50$
$\implies 17 - 11m = 50$

Step2: Isolate the variable term

$-11m = 50 - 17$
$\implies -11m = 33$

Step3: Solve for $m$

$m = \frac{33}{-11}$
$\implies m = -3$

Problem 7

Step1: Translate verbal to equation

Let the number be $n$. "Twice a number" is $2n$, "plus 5" is $+5$, "equal to 27" is $=27$.
$\implies 2n + 5 = 27$

Problem 8

Step1: Identify the unknown quantity

The question asks for miles traveled, so the variable represents miles.

Problem 9

Step1: Set up cost equation

Total cost = initial fee + (cost per mile × miles). Let $m$ = miles.
$\implies 1.5 + 1.5m = 21$

Answer:

1. B. 7
2. B. -3
3. D. $2n + 5 = 27$
4. C. $m =$ number of miles
5. C. $1.5m + 1.5 = 21$