Question

Solving Systems of Equations Approximately

Answer 1

The pattern is: The width of the first beach decreases by 2 feet every year and the width of the second beach increases by 5 feet each year (except from years 1995 to 2000 where it increases by 4 feet each year).

Answer 2

Thank you! :'D

Answer 3

You are welcome. Can you figure out B and C?

Answer 4

I think B is year 2006 right?

Answer 5

I'm lost for C

Answer 6

For B) Notice the width of the first beach is higher than that of the second and at one point the width of the second beach is higher than the first. So in between those two years the width must be the same. When does that happen? (Not 2006).

Answer 7

We need the correct answer for B before we can attempt C.

Answer 8

Um idk because in the chart no 2 are the same.

Answer 9

Year 11 (2006) it's 75 and 78 and that's the closest the widths of the two get.

Answer 10

Oops. I have been reading the year as 2011 instead of 11 years from 1995.
But they are asking between what two years they will be equal.
Until the year 2006, the width of the first beach is always greater than the width of the second beach. But in 2007, the width of the second beach is greater than the width of the first beach. So between the years: 2006 and 2007, their width must equal each other.

B) Between the years 2006 and 2007.

Answer 11

Oh okay :p

Answer 12

For C)
We found in part A, the width of first beach decreases by 2 feet each year and the width of the second beach increases by 5 feet each year. We know from part B the widths will be the same in between the years 2006 and 2007.
Take the data for the year 2006: first beach: 78 feet ; second beach: 75 feet.
Assume x years (x will be a fraction) after 2006 the beaches will have the same width.
Then 78 - 2x = 75 + 5x
solve for x.

Answer 13

x will be a fraction in years. Multiply by 12 to convert it to months. Approximately that many months into 2006, the two beaches will have the same width.

Answer 14

I don't understand the pattern for A

Answer 15

Beach #1:
Width decreases by: 10, 10, 2, 2, 6
Years increases by: 5, 5, 1, 1, 3
Divide 1st by 2nd: 2, 2, 2, 2, 2 (constant slope. change in y by change in x)

Answer 16

For beach 1, width decreases by 2 feet each year.

Answer 17

oh

Answer 18

i understand

Answer 19

Beach #2:
Width increases by: 20, 25, 5, 5, 15
Years increases by: 5, 5, 1, 1, 3
Divide 1st by 2nd: 4, 5, 5, 5, 5
(except for the first number. it is constant slope. change in y by change in x)
The width of the second beach increases by 5 feet per year.

Answer 20

78 - 2x = 75 + 5x
78-2x+2x=75+5x+2x
78=75+7x
78-75=7x
7x=3
x=2+1/3

Answer 21

^^^ 78-75=7x
3 = 7x
x = 3/7

Answer 22

3/7*12/1

36/7 = 5 1/7 months

Answer 23

Yes. Approximately 5 months into 2006, the two beaches will have the same width.

Answer 24

Or you can leave it as 5 and 1/7 months into 2006. (don't forget to include 2006)