Question

word problems
directions: for each problem, define a variable and set up an equation, then solve.

1. a bucket of raffle tickets was distributed evenly to 48 people. if each person got 4 tickets, how many tickets were in the bucket?
2. samantha withdrew $160 from her bank account. if the balance of the account is now $379.52, what was her balance before the withdrawal?
3. gas is $2.09 per gallon at the gas station. if nate filled up his car and spent $33.44, how many gallons did he put in his car?
4. in his last football game, sean rushed for 89 yards. if his season total is now 871 yards, how many total yards did he have prior to his last game?
5. while driving on the highway, mason put his car on cruise control at 68 miles per hour. at this speed, how long would it take him to drive 85 miles?
6. if the temperature is dropping at a rate of 2 degrees per hour, how many hours will it take to drop 15 degrees?
7. eight adult tickets to the amusement park cost $196. find the cost for each ticket.
8. tessa returned a book to the library 16 days late. if she was charged $0.35 per day, what was the total fine?
9. braden finished his math test 14 minutes before ariana did. if it took ariana 57 minutes, and they both started the test at the same time, how long did it take braden?
10. sarah and eva took a road trip. sarah drove two - fifths of the miles. if she drove 128 miles, how many total miles did they drive?

Explanation:

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Problem 1

Step1: Define variable

Let $B$ = total tickets in bucket

Step2: Set up equation

Total tickets = people × tickets per person:
$B = 48 \times 4$

Step3: Calculate solution

$B = 192$

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Problem 2

Step1: Define variable

Let $W$ = balance before withdrawal

Step2: Set up equation

Previous balance = new balance + withdrawal:
$W = 379.52 + 160$

Step3: Calculate solution

$W = 539.52$

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Problem 3

Step1: Define variable

Let $G$ = gallons of gas

Step2: Set up equation

Gallons = total cost ÷ price per gallon:
$G = \frac{33.44}{2.09}$

Step3: Calculate solution

$G = 16$

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Problem 4

Step1: Define variable

Let $Y$ = prior total yards

Step2: Set up equation

Prior yards = current total - new yards:
$Y = 871 - 89$

Step3: Calculate solution

$Y = 782$

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Problem 5

Step1: Define variable

Let $T$ = time in hours

Step2: Set up equation

Time = distance ÷ speed:
$T = \frac{85}{68}$

Step3: Calculate solution

$T = 1.25$

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Problem 6

Step1: Define variable

Let $H$ = hours to drop 15°

Step2: Set up equation

Hours = total drop ÷ rate per hour:
$H = \frac{15}{2}$

Step3: Calculate solution

$H = 7.5$

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Problem 7

Step1: Define variable

Let $C$ = cost per ticket

Step2: Set up equation

Cost per ticket = total cost ÷ tickets:
$C = \frac{196}{8}$

Step3: Calculate solution

$C = 24.50$

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Problem 8

Step1: Define variable

Let $F$ = total fine

Step2: Set up equation

Total fine = days late × fee per day:
$F = 16 \times 0.35$

Step3: Calculate solution

$F = 5.60$

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Problem 9

Step1: Define variable

Let $M$ = Braden's test time

Step2: Set up equation

Braden's time = Ariana's time - 14:
$M = 57 - 14$

Step3: Calculate solution

$M = 43$

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Problem 10

Step1: Define variable

Let $R$ = total road trip miles

Step2: Set up equation

$\frac{2}{5}R = 128$

Step3: Solve for $R$

$R = 128 \times \frac{5}{2}$
$R = 320$

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Answer:

1. Equation: $B=48 \times 4$; Solution: 192 tickets
2. Equation: $W=379.52+160$; Solution: $\$539.52$
3. Equation: $G=\frac{33.44}{2.09}$; Solution: 16 gallons
4. Equation: $Y=871-89$; Solution: 782 yards
5. Equation: $T=\frac{85}{68}$; Solution: 1.25 hours
6. Equation: $H=\frac{15}{2}$; Solution: 7.5 hours
7. Equation: $C=\frac{196}{8}$; Solution: $\$24.50$
8. Equation: $F=16 \times 0.35$; Solution: $\$5.60$
9. Equation: $M=57-14$; Solution: 43 minutes
10. Equation: $\frac{2}{5}R=128$; Solution: 320 miles