The questions are in the description Please help me I can't understand it.

Question

1. Find three consecutive integers such that five times the sum of the first and −4−4 is 3535 less than the sum of the second and third. Write the integers in order from least to greatest.
2. Mark and Amy live 435 miles apart. They are planning to meet somewhere between the two locations. If Mark travels at 60 mph and Amy travels at 45 mph, and Amy is planning on leaving two hours later than Mark, how many miles will Mark travel before they meet?
3. Find the distance between (2,−6)(2,−6) and (7,4)

Answer 1

1. Find three consecutive integers such that five times the sum of the first and −4 is 35 less than the sum of the second and third. Write the integers in order from least to greatest.

Use a, b, and c for the consecutive integers.

b = a+1

c = a+2

"five times the sum of the first and −4 is 35 less than the sum of the second and third" means

5*(a + (-4)) = (b+c) - 35

5(a-4) = ( (a+1) + (a+2) ) - 35

5a - 20 = 2a - 32

3a = -12

a = -4

b = -3

c = -2

Note that: -4 < -3 < -2

1. Mark and Amy live 435 miles apart. They are planning to meet somewhere between the two locations. If Mark travels at 60 mph and Amy travels at 45 mph, and Amy is planning on leaving two hours later than Mark, how many miles will Mark travel before they meet?

The total distance (435) is known. We must find distance d.

If Mark leaves at t=0, Amy leaves at t=2, so het time spent is T-2.

Distance = Rate * Time [Remember Distance is Rate times Time (D-I-R-T)

We must first find time.

MarkDist + AmyDist = 435

60*T + 45*(T-2) = 435

60T + 45T - 90 = 435

105T = 525

T = 5 hours

In 5 hours, Mark travels 300 miles.

Check:

In 3 hours (1hour for Amy),, Amy travels 135 miles.

Total = 435 miles.

1. Find the distance between (2,−6)(2,−6) and (7,4)

Use the Distance Formula:

d = √( (x₂- x₁)² + (y₂-y₁)² )

d = √ (7-2)² + (4-(-6))² )

d = √ (5)² + (10)² )

d = √ (25 + 100)

d = √125

d = 11.18034 (You should round it)

Answer 2

If the consecutive numbers are: a,b,c

You will write it out in an equation to express it:

5a(-4-4)= 3535-(b+c)

When trying to solve algebraic expressions, substitution and re-expressing words for symbols are so important.

IS usually denotes = or equal sign, LESS means subtract and AND means add. The word TIMES means multiply.

So the above equation is what you would start off with to express the word problem as an equation.

Now if you can use substitution to express these three integers in terms of one another and just solve for one integer, you can find these other two integers.

a,b,c

We are told that they are consecutive numbers in a series so:

If a =x, b=x+1, and c=x+2.

Now we can substitute everything in and solve for just one integer, x:

5a(-4-4)= 3535-(b+c)

SUBSTITUTION

5x(-4-4)= 3535-((x+1)+(x+2))

Now you solve for X:

5x(-8)= 3535-((x+1)+(x+2))

-40x= 3535- 2x+3

Using PEMDAS will help you simplify accurately.

Now we can combine like terms:

Notice the -2x on the right, when it comes over to the left it needs to be added to the -40x and you have:

-38x= 3535+ 3

-38x= 3538

x=3538/-38

x= approximately -93, you would have to round down because the 0.1 makes it most close to 93 as an integer.

Now that you have your x value, you can plug in this number and find what the other numbers would have to be.

x=-93 for a, b= -93+1 or -92 and c= -93+2, or -91.

So your series of numbers would look like:

-93,-92,-91

And because they did not indicate whether this is an ascending or descending order, it is still correct following the number line, these are 3 consecutive numbers.