Question

I am confused on this problem
the number of years a person born in the united states is expected to live can approximated by the equation y= 0.189x +70.8 where x is the number of years since 1970 solve the equation for x use this new equation to determine in which year the approximate life expectancy will be 80.2 years.

Answer 1

solve the equation for x

y= 0.189x +70.8

what do you get if you add -70.8 to both sides ?

Answer 2

I would get -70.8y = 0.189

Answer 3

add -70.8 to both sides. to do this, write -70.8 on both sides, like this

y-70.8 = 0.189x +70.8-70.8

now simplify the right side. what is 70.8 - 70.8 ?

Answer 4

that is 0

Answer 5

yes, so the equation is now
y-70.8 = 0.189x
or
0.189 x = y-70.8

now divide both sides by 0.189
\[ \frac{0.189 x}{0.189}= \frac{y-70.8}{0.189 } \]
the 0.189 divided by itself is 1 so the left side simplifies to 1 times x or just x
you now have
\[ x= \frac{y-70.8}{0.189 }\]

now find x when y is 80.2
can you do that ?

Answer 6

I get these numbers -374.6031746

Answer 7

when I divide -70.8 by 0.189

Answer 8

you start with the equation
\[ x= \frac{y-70.8}{0.189 }\]

the problem asks for x when y is 80.2 (it is not clearly written out, but they say y=80.2)
so erase the y in the equation, and put in 80.2 in its place
can you do that ?

Answer 9

ok I got that now do I do what we just did just use 80.2 this time

Answer 10

erase the y in the equation, and put in 80.2 in its place
what is the equation after you do that ?

Answer 11

80.2 = 0.189x + 70.8

Answer 12

ok, but we want to use the equation where we solved for x.
\[ x= \frac{y-70.8}{0.189 }\]

Answer 13

ok so is that the equation

Answer 14

yes. the problem said

solve the equation for x
use this new equation

so you want to use this new equation. can you replace y with 80.2 ?
what does the equation look like after you do that ?

Answer 15

0.189x = 80.2 + 70.8

Answer 16

replace y with 80.2 in
\[ x= \frac{y-70.8}{0.189 }\]

Answer 17

x= -70.8(80.2)/0.189

Answer 18

no, but that is closer.
do this
\[ x= \frac{\cancel{y}80.2-70.8}{0.189 } \\
x= \frac{80.2-70.8}{0.189 }
\]

Answer 19

I don't have a calculator that dose all that

Answer 20

that's why I am doing it by hand

Answer 21

ok I got x =92/0.189

Answer 22

do it in steps. what is 80.2 - 70.8
you can type it into google, like this
80.2 - 70.8=

Answer 23

80 - 70 is 10 so 80.2 - 70.8 will be close to 10

Answer 24

ok so is it x = 10/0.189

Answer 25

almost 10. type into google this
80.2 - 70.8=
what do you get ?

Answer 26

ok hang on

Answer 27

9.4 is what I got

Answer 28

so now the equation is
x= 9.4/0.189

can you find x ?

Answer 29

\[ x= \frac{80.2-70.8}{0.189 } \\
x= \frac{9.4}{0.189 } = ?\]

Answer 30

you can use google again, if you like:
9.4/0.189=

Answer 31

ok I got 49. 735449

Answer 32

you got x= 49.7 (roughly)

the problem says x is the number of years since 1970
what year is that ? I would do 1970+ x to find out.

Answer 33

so x= 2019

Answer 34

to be accurate, x is 49.7 years, and the date is (1970 + x) = 2019.7

the answer to
determine in which year the approximate life expectancy will be 80.2 years.
is 2019

Answer 35

ok thank you for the help