Question

Arnold's company reimburses his expenses on food, lodging, and conveyance during business trips. The company pays $40 a day for food and lodging and $0.50 for each mile traveled. Arnold drove 400 miles and was reimbursed $2600.

Part A: Create an equation that will determine the number of days x on the trip (3 points)

Part B: Solve this equation justifying each step with an algebraic property of equality. (6 points)

Part C: How many days did Arnold spend on this trip? (1 points)

Answer 1

food+lodging = $40 per day
conveyance = $0.5 per mile

Answer 2

Since he drove 400 miles, how much he wud get for conveyance ?

Answer 3

240 total

Answer 4

200 for the conveyance

Answer 5

Yes, 200 for conveyance

Answer 6

say he was on trip for \(x\) days

Answer 7

for part A,
can u setup an equation with the info above ?

Answer 8

if he was on trip for \(x\) days, then he wud get \(40x\) dollars

Answer 9

40x+200=2600

Answer 10

and since he got 200 $ for the conveyance,
the equation wud be :-

\(40x + 200 = 2600\)

Answer 11

:)

Answer 12

try part B,
its tricky cuz u need to justify EACH step

Answer 13

40x+200=2600
Take 200 away from each side
40x+200-200=2600-200
You will then be left with
40x=2400
Divide by 40 on each side
40x/40=2400/40
You will then be left with
x=60

Answer 14

looks good ,
but i dont see any algebraic properties used

Part B: Solve this equation justifying each step with an \(\color{red}{algebraic ~~property}\) of equality. (6 points)

Answer 15

40x+200=2600

40x+200 - 200 = 2600 - 200 (By subtraction property of equality)

40x = 2400

40x/40 = 2400/40 (By division property of equality)

x = 60

Answer 16

your teacher will be looking for those two property names :o

Answer 17

So subtraction can be first?

Answer 18

"subtraction property of equality"

Answer 19

Yes, but subtraction can go before division?

Answer 20

Yes why not

Answer 21

why do u ask that ?

Answer 22

40x+200=2600

when u have equation like above,
subtracting 200 is the first thing u want to do. doing anything else is simply ridiculous

Answer 23

you can divide 40 both sides, but if u do that, u wil have to divide two times, one time for 200 and second time for 2600... so just do subtraction first

Answer 24

PEDMAS

Answer 25

we're still sticking to PEMDAS.
but when solving equations, NEVER FOLLOW PEMDAS order.

Answer 26

40x+200=2600

you DONT need to divide 40 first

Answer 27

you can subtract 200 first, cuz its easy to do here

Answer 28

lets do it both ways, and see if we can convince ourself if we get both answers same ?

Answer 29

40x+200=2600

using PEMDAS order
```
40x+200=2600

divide 40 both sides

x + 5 = 65

subtract 5 both sides

x = 60
```

without using PEMDAS
```
40x+200=2600

subtract 200 both sides

40x = 2400

divide 40 both sides

x = 60
```

Answer 30

Ok I'll do what we first did then :)

Answer 31

good :)