Question

At Eric's auto shop, it takes him
15
minutes to do an oil change and
24
minutes to do a tire change. Let
x
be the number of oil changes he does. Let
y
be the number of tire changes he does.
Using the values and variables given, write an inequality describing how many oil changes and tire changes Eric can do in less than
3
hours (
180
minutes).

Answer 1

each oil change takes him 15 minutes
if he does "x" number of oil changes, how much time he takes ?

Answer 2

Excellent! but thats not the exact answer
just look at the wording in problem, they want an inequality right ?

"less than 180 minutes"

Answer 3

15x+24y>180

Answer 4

thats the expression for the combined works that take him MORE than 180 minutes

try again

Answer 5

so switch the sign <

Answer 6

thats it! part of the solution for word problems lies in interpreting the problem correctly

Answer 7

i suck at word problems

Answer 8

so 15x+24y<180

Answer 9

yes!
i follow below steps while working word problems see if it helps :
1) read the problem once
2) write out all the given info
3) read the problem again
4) write down what they are asking you to find out
5) find it

Answer 10

Omar and Ryan each ran every day as part of an exercise routine. Omar ran
3
miles each day for
x
days. Ryan ran
4
miles each day for
y
days.
The total number of miles that Omar ran is at least the total number of miles that Ryan ran. Write an inequality describing this relationship.

Answer 11

so far 3x+4y

Answer 12

this is a slightly different problem, lets go step by step

Answer 13

ook

Answer 14

Omar :
each day he runs 3 miles
so how many miles does he run in x days ?

Ryan :
each day he runs 4 miles
so how many miles does he run in y days ?

Answer 15

hmm

Answer 16

to tell u the truth im still confused on this one

Answer 17

its okay, it has to be confusing in the start because there are two different people in this word problem

Answer 18

Omar :
each day he runs 3 miles
so how many miles does he run in x days ? `3x`

Ryan :
each day he runs 4 miles
so how many miles does he run in y days ? `4y`

Answer 19

i got that far on it

Answer 20

Good, so far we have :

Omar runs `3x` miles in total

Ryan runs `4y` miles in total

Answer 21

lets see what exactly the problem is asking us to find out

Answer 22

The total number of miles that Omar ran is at least the total number of miles that Ryan ran. Write an inequality describing this relationship.

Answer 23

`The total number of miles that Omar ran` is at least `the total number of miles that Ryan ran.`

can we translate this sentence into

`3x` >= `4y`

?

Answer 24

so 3x> with the line under it 4y

Answer 25

yes thats it!

Answer 26

o my god thank you so much

Answer 27

yeay more

Answer 28

Kaitlin works as a tutor for
$7
an hour and as a waitress for
$11
an hour. This month, she worked a combined total of
107
hours at her two jobs.
Let
t
be the number of hours Kaitlin worked as a tutor this month. Write an expression for the combined total dollar amount she earned this month.

Answer 29

give it a try

Answer 30

start by writing down given info and making sense of the scenario in problem..

Answer 31

Kaitlin works as a tutor for waitress for
$7 $11
total work for both jobs 107

Answer 32

7t+11=107

Answer 33

thats a very good try !

Answer 34

we know that she worked a total of 107 hours

lets say she tutored `t` hours ,
that means she must have waitressed for `107-t` hours

yes ?

Answer 35

yes

Answer 36

so amount from tutoring = `7t`

amount from waitressing = `11(107-t)`

Answer 37

add them up for the total amount that she gets this month

Answer 38

by add them up, i mean just put a "+" sign between them :)

Answer 39

7t+11(107-t)

Answer 40

Looks perfect!
simplify if you want.. but it shouldn't matter..

Answer 41

if you want a good laugh ;p