6. mark flew from boston to baltimore, then baltimore to orlando. the number of people on his first flight was five more than four times the number of people on his second flight. if there were 365 people altogether on the two flights, how many were on the flight from baltimore to orlando?
7. morgan is making two cookie recipes. recipe a calls for one - third less than twice the number of cups of sugar that recipe b calls for. if she needs four and one - sixths cups of sugar in all, how many cups will she need for recipe a?
8. on the album \1989\ by taylor swift, blank space is 12 seconds longer than shake it off. if the combined time of the two songs is 7 minutes and 30 seconds, how long is shake it off? give your answer in minutes and seconds.
9. rachel took a two - day road trip last weekend. she drove 65 miles less on sunday than she did on saturday. if twice the miles driven on sunday is 373 more than the number of miles driven on saturday, how many miles did she drive each day?
10. the sum of two consecutive integers is 129. find both integers.

Question

Accepted Answer

### Problem 10: The sum of two consecutive integers is 129. Find both integers.
# Explanation:
## Step1: Define the variables
Let the first integer be $ x $. Then the next consecutive integer is $ x + 1 $.
## Step2: Set up the equation
The sum of the two consecutive integers is 129, so we have the equation $ x + (x + 1) = 129 $.
## Step3: Solve the equation
Simplify the left side: $ 2x + 1 = 129 $.
Subtract 1 from both sides: $ 2x = 129 - 1 = 128 $.
Divide both sides by 2: $ x = \frac{128}{2} = 64 $.
## Step4: Find the second integer
The second integer is $ x + 1 = 64 + 1 = 65 $.
# Answer:
The two consecutive integers are 64 and 65.

### Problem 9: Rachel took a two - day road trip last weekend. She drove 65 miles less on Saturday than on Sunday. If twice the miles driven on Sunday is 373 more than the number of miles driven on Saturday, how many miles did she drive each day?
# Explanation:
## Step1: Define the variables
Let the number of miles driven on Sunday be $ x $. Then the number of miles driven on Saturday is $ x - 65 $.
## Step2: Set up the equation
Twice the miles driven on Sunday is 373 more than the miles driven on Saturday, so $ 2x=(x - 65)+373 $.
## Step3: Solve the equation
Simplify the right side: $ 2x=x + 373-65=x + 308 $.
Subtract $ x $ from both sides: $ 2x-x=308 $, so $ x = 308 $.
## Step4: Find the miles driven on Saturday
The miles driven on Saturday is $ x - 65=308 - 65 = 243 $.
# Answer:
She drove 243 miles on Saturday and 308 miles on Sunday.

### Problem 8: On the album "1989" by Taylor Swift, Blank Space is 12 seconds longer than Shake It Off. If the combined time of the two songs is 7 minutes and 30 seconds, how long is Shake It Off? Give your answer in minutes and seconds.
# Explanation:
## Step1: Convert the total time to seconds
7 minutes and 30 seconds is equal to $ 7\times60 + 30=420+30 = 450 $ seconds.
## Step2: Define the variables
Let the time of Shake It Off be $ x $ seconds. Then the time of Blank Space is $ x + 12 $ seconds.
## Step3: Set up the equation
The sum of their times is 450 seconds, so $ x+(x + 12)=450 $.
## Step4: Solve the equation
Simplify the left side: $ 2x+12 = 450 $.
Subtract 12 from both sides: $ 2x=450 - 12=438 $.
Divide both sides by 2: $ x=\frac{438}{2}=219 $ seconds.
## Step5: Convert 219 seconds to minutes and seconds
Divide 219 by 60: $ 219\div60 = 3$ minutes with a remainder of $ 219-3\times60=219 - 180 = 39 $ seconds.
# Answer:
Shake It Off is 3 minutes and 39 seconds long.

### Problem 7: Morgan is making two cookie recipes. Recipe A calls for one - third less than twice the number of cups of sugar that Recipe B calls for. If she needs four and one - sixths cups of sugar in all, how many cups will she need for Recipe A?
# Explanation:
## Step1: Define the variables
Let the number of cups of sugar for Recipe B be $ x $. Then the number of cups of sugar for Recipe A is $ 2x-\frac{1}{3}x=\frac{6x - x}{3}=\frac{5x}{3} $.
## Step2: Set up the equation
The total number of cups of sugar is $ 4\frac{1}{6}=\frac{25}{6} $ cups. So $ x+\frac{5x}{3}=\frac{25}{6} $.
## Step3: Solve the equation
Find a common denominator for the left side: $ \frac{3x+5x}{3}=\frac{8x}{3} $.
We have $ \frac{8x}{3}=\frac{25}{6} $. Cross - multiply: $ 8x\times6 = 25\times3 $, $ 48x = 75 $, $ x=\frac{75}{48}=\frac{25}{16}=1\frac{9}{16} $ cups.
## Step4: Find the number of cups for Recipe A
$ \frac{5x}{3}=\frac{5}{3}\times\frac{25}{16}=\frac{125}{48}=2\frac{29}{48} $ cups. Or we can do it another way:
From $ x+\frac{5x}{3}=\frac{25}{6} $, $ \frac{8x}{3}=\frac{25}{6} $, $ x=\frac{25}{6}\times\frac{3}{8}=\frac{25}{16} $. Then Recipe A: $ 2\times\frac{25}{16}-\frac{1}{3}\times\frac{25}{16}=\frac{50}{16}-\frac{25}{48}=\frac{150 - 25}{48}=\frac{125}{48}=2\frac{29}{48} \approx 2.604 $ cups. Also, $ 4\frac{1}{6}=\frac{25}{6} $, and if we let Recipe B be $ x $, Recipe A is $ \frac{5x}{3} $, $ x+\frac{5x}{3}=\frac{8x}{3}=\frac{25}{6} $, $ x=\frac{25}{16} $, Recipe A: $ \frac{5}{3}\times\frac{25}{16}=\frac{125}{48}=2\frac{29}{48} $ cups.
# Answer:
She will need $ 2\frac{29}{48} $ (or approximately $ 2.60 $) cups for Recipe A.

### Problem 6: Mark flew from Boston to Baltimore, then Baltimore to Orlando. The number of people on his first flight was five more than four times the number of people on his second flight. If there were 365 people altogether on the two flights, how many were on the flight from Baltimore to Orlando?
# Explanation:
## Step1: Define the variables
Let the number of people on the flight from Baltimore to Orlando (second flight) be $ x $. Then the number of people on the first flight is $ 4x + 5 $.
## Step2: Set up the equation
The total number of people on the two flights is 365, so $ (4x + 5)+x=365 $.
## Step3: Solve the equation
Simplify the left side: $ 5x+5 = 365 $.
Subtract 5 from both sides: $ 5x=365 - 5 = 360 $.
Divide both sides by 5: $ x=\frac{360}{5}=72 $.
# Answer:
There were 72 people on the flight from Baltimore to Orlando.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 10: The sum of two consecutive integers is 129. Find both integers.

Step1: Define the variables

Step2: Set up the equation

Step3: Solve the equation

Step4: Find the second integer

Step1: Define the variables

Step2: Set up the equation

Step3: Solve the equation

Step4: Find the miles driven on Saturday

Step1: Convert the total time to seconds

Step2: Define the variables

Step3: Set up the equation

Step4: Solve the equation

Step5: Convert 219 seconds to minutes and seconds

Answer:

Problem 9: Rachel took a two - day road trip last weekend. She drove 65 miles less on Saturday than on Sunday. If twice the miles driven on Sunday is 373 more than the number of miles driven on Saturday, how many miles did she drive each day?